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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 2(200), Pages 85–134 (Mi umn3391)  

This article is cited in 222 scientific papers (total in 222 papers)

The geometry of toric varieties

V. I. Danilov

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English version:
Russian Mathematical Surveys, 1978, 33:2, 97–154

Bibliographic databases:

UDC: 513.015.7
MSC: 14M25, 14R10, 14C15, 14C17, 14F43, 14F25
Received: 05.10.1977

Citation: V. I. Danilov, “The geometry of toric varieties”, Uspekhi Mat. Nauk, 33:2(200) (1978), 85–134; Russian Math. Surveys, 33:2 (1978), 97–154

Citation in format AMSBIB
\by V.~I.~Danilov
\paper The geometry of toric varieties
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 2(200)
\pages 85--134
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 2
\pages 97--154

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    1. V. I. Danilov, “Newton polyhedra and vanishing cohomology”, Funct. Anal. Appl., 13:2 (1979), 103–115  mathnet  crossref  mathscinet  zmath
    2. Richard P Stanley, “The number of faces of a simplicial convex polytope”, Advances in Mathematics, 35:3 (1980), 236  crossref
    3. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi
    4. V. V. Batyrev, “Toroidal Fano 3-folds”, Math. USSR-Izv., 19:1 (1982), 13–25  mathnet  crossref  mathscinet  zmath
    5. È. B. Vinberg, “Absence of crystallographic groups of reflections in Lobachevskii spaces of large dimension”, Funct. Anal. Appl., 15:2 (1981), 128–130  mathnet  crossref  mathscinet  zmath  isi
    6. V. E. Voskresenskii, “Projective invariant Demazure models”, Math. USSR-Izv., 20:2 (1983), 189–202  mathnet  crossref  mathscinet  zmath
    7. V. I. Danilov, “Birational geometry of toric 3-folds”, Math. USSR-Izv., 21:2 (1983), 269–280  mathnet  crossref  mathscinet  zmath
    8. I.M Gelfand, R.D MacPherson, “Geometry in Grassmannians and a generalization of the dilogarithm”, Advances in Mathematics, 44:3 (1982), 279  crossref
    9. Franz Pauer, “Glatte Einbettungen vonG/U”, Math Ann, 262:3 (1983), 421  crossref  mathscinet  zmath  isi
    10. V. E. Voskresenskii, A. A. Klyachko, “Toroidal Fano varieties and root systems”, Math. USSR-Izv., 24:2 (1985), 221–244  mathnet  crossref  mathscinet  zmath
    11. Günter Ewald, “CONVEX BODIES AND ALGEBRAIC GEOMETRY”, Ann N Y Acad Sci, 440:1 discrete (1985), 196  crossref  mathscinet  isi
    12. Richard P. Stanley, “THE NUMBER OF FACES OF SIMPLICIAL POLYTOPES AND SPHERES”, Ann N Y Acad Sci, 440:1 discrete (1985), 212  crossref  mathscinet  zmath  isi
    13. D. G. Markushevich, “Canonical singularities of three-dimensional hypersurfaces”, Math. USSR-Izv., 26:2 (1986), 315–345  mathnet  crossref  mathscinet  zmath
    14. È. B. Vinberg, “Hyperbolic reflection groups”, Russian Math. Surveys, 40:1 (1985), 31–75  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. A. A. Klyachko, “Orbits of a maximal torus on a flag space”, Funct. Anal. Appl., 19:1 (1985), 65–66  mathnet  crossref  mathscinet  zmath  isi
    16. G. K. Sankaran, “Effective resolution of cusps on Hilbert modular varieties”, Math Proc Camb Phil Soc, 99:1 (1986), 51  crossref  mathscinet  zmath  isi
    17. V. I. Danilov, A. G. Khovanskii, “Newton polyhedra and an algorithm for computing Hodge–Deligne numbers”, Math. USSR-Izv., 29:2 (1987), 279–298  mathnet  crossref  mathscinet  zmath
    18. A. G. Khovanskii, “Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskii space”, Funct. Anal. Appl., 20:1 (1986), 41–50  mathnet  crossref  mathscinet  zmath  isi
    19. Elisabetta Stricland, “A vanishing theorem for group compactifications”, Math Ann, 277:1 (1987), 165  crossref  mathscinet  isi
    20. Alan Adolphson, Steven Sperber, “Newton polyhedra and the degree of theL-function associated to an exponential sum”, Invent math, 88:3 (1987), 555  crossref  mathscinet  zmath  adsnasa  isi
    21. Richard P. Stanley, “On the number of faces of centrally-symmetric simplicial polytopes”, Graphs Comb, 3:1 (1987), 55  crossref  mathscinet  zmath  isi
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    25. I. D. Gubeladze, “Anderson's conjecture and the maximal monoid class over which projective modules are free”, Math. USSR-Sb., 63:1 (1989), 165–180  mathnet  crossref  mathscinet  zmath
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    134. A.L. Kholodenko, “New strings for old Veneziano amplitudes”, Journal of Geometry and Physics, 56:9 (2006), 1433  crossref
    135. Osamu Fujino, “Multiplication maps and vanishing theorems for Toric varieties”, Math Z, 257:3 (2007), 631  crossref  mathscinet  zmath  isi
    136. Volker Braun, Burt A Ovrut, Maximilian Kreuzer, Emanuel Scheidegger, “Worldsheet instantons and torsion curves. Part B: mirror symmetry”, J High Energy Phys, 2007:10 (2007), 023  crossref  mathscinet
    137. B. Ya. Kazarnovskii, “Multiplicative intersection theory and complex tropical varieties”, Izv. Math., 71:4 (2007), 673–720  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    138. Przyjalkowski V., “On Landau-Ginzburg models for Fano varieties”, Communications in Number Theory and Physics, 1:4 (2007), 713–728  isi
    139. Nicole Berline, Michèle Vergne, “The equivariant Todd genus of a complete toric variety, with Danilov condition”, Journal of Algebra, 313:1 (2007), 28  crossref
    140. Xuejun Wang, Stephen Yau, “On the GLY Conjecture of upper estimate of positive integral points in real right-angled simplices”, Journal of Number Theory, 122:1 (2007), 184  crossref
    141. Goldin R., Holm T.S., Knutson A., “Orbifold Cohomology of Torus Quotients”, Duke Math. J., 139:1 (2007), 89–139  crossref  isi
    142. V. V. Przyjalkowski, “Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties”, Sb. Math., 198:9 (2007), 1325–1340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    143. N. Berline, M. Vergne, “Local Euler–Maclaurin formula for polytopes”, Mosc. Math. J., 7:3 (2007), 355–386  mathnet  crossref  mathscinet  zmath
    144. Lex E. Renner, “Descent systems for Bruhat posets”, J Algebr Comb, 2008  crossref  mathscinet  isi
    145. Lex E. Renner, “Rationally smooth algebraic monoids”, Semigroup Forum, 2008  crossref  mathscinet  isi
    146. T. E. Panov, “Toric Kempf–Ness Sets”, Proc. Steklov Inst. Math., 263 (2008), 150–162  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    147. Anvar R Mavlyutov, “Cohomology of rational forms and a vanishing theorem on toric varieties”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2008:615 (2008), 45  crossref
    148. Lex E. Renner, “The H-polynomial of a semisimple monoid”, Journal of Algebra, 319:1 (2008), 360  crossref
    149. Buchstaber V.M., Ray N., “An invitation to toric topology: Vertex four of a remarkable tetrahedron”, Toric Topology, Contemporary Mathematics Series, 460, 2008, 1–27  isi
    150. Hamilton M.D., “The Quantization of a Toric Manifold Is Given by the Integer Lattice Points in the Moment Polytope”, Toric Topology, Contemporary Mathematics Series, 460, eds. Harada M., Karshon Y., Masuda M., Panov T., Amer Mathematical Soc, 2008, 131–140  isi
    151. Holm T.S., “Act Globally, Compute Locally: Group Actions, Fixed Points, and Localization”, Toric Topology, Contemporary Mathematics Series, 460, eds. Harada M., Karshon Y., Masuda M., Panov T., Amer Mathematical Soc, 2008, 179–195  isi
    152. Oleg Karpenkov, “On irrational lattice angles”, Funct Anal Other Math, 2009  crossref  mathscinet
    153. Thomas Hüttemann, “K-Theory of non-linear projective toric varieties”, form, 21:1 (2009), 67  crossref  mathscinet  zmath  isi
    154. JOHANNES J. DUISTERMAAT, ALVARO PELAYO, “Reduced phase space and toric variety coordinatizations of Delzant spaces”, Math Proc Camb Phil Soc, 2009, 1  crossref  mathscinet  isi
    155. Klaus Altmann, Duco Straten, “Smoothing of quiver varieties”, manuscripta math, 2009  crossref  mathscinet  isi
    156. Paul Hacking, Sean Keel, Jenia Tevelev, “Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces”, Invent math, 2009  crossref  mathscinet  isi
    157. Lev Borisov, Zheng Hua, “On the conjecture of King for smooth toric Deligne–Mumford stacks”, Advances in Mathematics, 221:1 (2009), 277  crossref
    158. Diego Ruano, “On the structure of generalized toric codes”, Journal of Symbolic Computation, 44:5 (2009), 499  crossref
    159. Asok A., Doran B., “A(1)-Homotopy Groups, Excision, and Solvable Quotients”, Adv. Math., 221:4 (2009), 1144–1190  crossref  isi
    160. Ostrover Ya., Tyomkin I., “On the Quantum Homology Algebra of Toric Fano Manifolds”, Sel. Math.-New Ser., 15:1 (2009), 121–149  crossref  isi
    161. Mullet J.P., “Toric Calabi-Yau Hypersurfaces Fibered by Weighted K3 Hypersurfaces”, Commun. Anal. Geom., 17:1 (2009), 107–138  isi
    162. Hal Schenck, “Euler characteristic of coherent sheaves on simplicial torics via the Stanley–Reisner ring”, J Math Phys (N Y ), 51:11 (2010), 112304  crossref
    163. Bahri A., Bendersky M., Cohen F.R., Gitler S., “The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces”, Advances in Mathematics, 225:3 (2010), 1634–1668  crossref  isi  elib
    164. J.R. Maurício Corrêa, “Darboux–Jouanolou–Ghys integrability for one-dimensional foliations on toric varieties”, Bulletin des Sciences Mathématiques, 134:7 (2010), 693  crossref
    165. Martin Weimann, “A lifting and recombination algorithm for rational factorization of sparse polynomials”, Journal of Complexity, 26:6 (2010), 608  crossref
    166. Jonathan Browder, “Representations of cyclic groups acting on complete simplicial fans”, Journal of Combinatorial Theory, Series A, 117:6 (2010), 766  crossref
    167. Pelayo A., “Introduction”, Mem. Am. Math. Soc., 204:959 (2010), 1+  crossref  isi
    168. Banagl M., “Homotopy Theory”, Intersection Spaces, Spatial Homology Truncation, and String Theory, Lect. Notes Math., 1997, Springer-Verlag Berlin, 2010, 1+  crossref  isi
    169. Jan-Li Lin, “Algebraic stability and degree growth of monomial maps”, Math. Z, 2011  crossref
    170. C. Concini, C. Procesi, M. Vergne, “Infinitesimal index: cohomology computations”, Transformation Groups, 2011  crossref
    171. Martin Weimann, “Concavity, Abel transform and the Abel-inverse theorem in smooth complete toric varieties”, Collect. Math, 2011  crossref
    172. V. M. Buchstaber, V. D. Volodin, “Sharp upper and lower bounds for nestohedra”, Izv. Math., 75:6 (2011), 1107–1133  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    173. Fu Liu, “Higher integrality conditions, volumes and Ehrhart polynomials”, Advances in Mathematics, 226:4 (2011), 3467  crossref
    174. Lex E. Renner, “The H-polynomial of an irreducible representation”, Journal of Algebra, 332:1 (2011), 159  crossref
    176. Baier T., Florentino C., Mourao J.M., Nunes J.P., “Toric Kahler Metrics Seen From Infinity, Quantization and Compact Tropical Amoebas”, J. Differ. Geom., 89:3 (2011), 411–454  isi
    177. Andreas Hochenegger, “Exceptional sequences of line bundles and spherical twists: a toric example”, Beitr Algebra Geom, 2012  crossref
    178. S. E. Parkhomenko, “Fermionic screenings and line bundle twisted chiral de Rham complex on CY manifolds”, J. Exp. Theor. Phys, 114:1 (2012), 39  crossref
    179. Martin Weimann, “Algebraic Osculation and Application to Factorization of Sparse Polynomials”, Found Comput Math, 2012  crossref
    180. Taras Panov, Yuri Ustinovsky, “Complex-analytic structures on moment-angle manifolds”, Mosc. Math. J., 12:1 (2012), 149–172  mathnet  crossref  mathscinet
    181. Bong H. Lian, Shing-Tung Yau, “Period integrals of CY and general type complete intersections”, Invent. math, 2012  crossref
    182. Yu. Li, “On transition functions of Topological Toric Manifolds”, Dalnevost. matem. zhurn., 12:1 (2012), 35–47  mathnet
    183. Letitia Golubitsky, “Betti Numbers of Toric Varieties and Eulerian Polynomials”, Communications in Algebra, 40:6 (2012), 2091  crossref
    184. UGO BRUZZO, ANTONELLA GRASSI, “PICARD GROUP OF HYPERSURFACES IN TORIC 3-FOLDS”, Int. J. Math, 23:02 (2012), 1250028  crossref
    185. Alexandre G. Aleksandrov, “Lʼindice topologique des champs de vecteurs sur les intersections complètes quasi-homogènes”, Comptes Rendus Mathematique, 2012  crossref
    186. Donu Arapura, Parsa Bakhtary, Jarosław Włodarczyk, “Weights on cohomology, invariants of singularities, and dual complexes”, Math. Ann, 2013  crossref
    187. T. E. Panov, “Geometric structures on moment-angle manifolds”, Russian Math. Surveys, 68:3 (2013), 503–568  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    188. Qihong Xie, “Vanishing theorems on toric varieties in positive characteristic”, Math. Z, 2013  crossref
    189. Kevin Langlois, “Clôture intégrale et opérations de tores algébriques de complexité un dans les variétés affines”, Transformation Groups, 2013  crossref
    190. L. Astey, A. Bahri, M. Bendersky, F.R. Cohen, D.M. Davis, “The -rings of , the Davis–Januszkiewicz spaces and certain toric manifolds”, Journal of Pure and Applied Algebra, 2013  crossref
    191. Trans. Moscow Math. Soc., 74 (2013), 203–216  mathnet  crossref  mathscinet  zmath  elib
    192. Esterov A., “The Discriminant of a System of Equations”, Adv. Math., 245 (2013), 534–572  crossref  isi
    193. J. Math. Sci. (N. Y.), 199:3 (2014), 302–305  mathnet  crossref
    194. S.E. Parkhomenko, “Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds”, Nuclear Physics B, 2014  crossref
    195. Hajime Fujita, Mikio Furuta, Takahiko Yoshida, “Torus Fibrations and Localization of Index II”, Commun. Math. Phys, 2014  crossref
    196. JETP Letters, 99:1 (2014), 42–46  mathnet  crossref  crossref  isi  elib  elib
    197. Luo Sh., Matsumura T., Moore W.F., “Moment Angle Complexes and Big Cohen-Macaulayness”, Algebr. Geom. Topol., 14:1 (2014), 379–406  crossref  isi
    198. João.P.. Nunes, “Degenerating Kähler structures and geometric quantization”, Rev. Math. Phys, 2014, 1430009  crossref
    199. L. G. Maxim, J. Schürmann, “Characteristic Classes of Singular Toric Varieties”, Commun. Pur. Appl. Math, 2014, n/a  crossref
    200. M. M. Graev, “Einstein equations for invariant metrics on flag spaces and their Newton polytopes”, Trans. Moscow Math. Soc., 75 (2014), 13–68  mathnet  crossref  elib
    201. Proc. Steklov Inst. Math., 286 (2014), 324–344  mathnet  crossref  crossref  isi  elib  elib
    202. Yu. M. Ustinovsky, “Geometry of compact complex manifolds with maximal torus action”, Proc. Steklov Inst. Math., 286 (2014), 198–208  mathnet  crossref  crossref  isi  elib
    203. A. P. Braun, T. Watari, “The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications”, J. High Energ. Phys, 2015:1 (2015)  crossref
    204. Kim, “On the integral cohomology of toric varieties”, J. Algebra Appl, 2015, 1650032  crossref
    205. V. M. Buchstaber, A. A. Kustarev, “Embedding theorems for quasi-toric manifolds given by combinatorial data”, Izv. Math., 79:6 (2015), 1157–1183  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    206. G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    207. A. G. Aleksandrov, “The Index of Differential Forms on Complete Intersections”, Funct. Anal. Appl., 49:1 (2015), 1–14  mathnet  crossref  crossref  zmath  isi  elib
    208. Battaglia F., Zaffran D., “Foliations Modeling Nonrational Simplicial Toric Varieties”, no. 22, 2015, 11785–11815  crossref  isi
    209. A. G. Aleksandrov, “Differential Forms on Quasihomogeneous Noncomplete Intersections”, Funct. Anal. Appl., 50:1 (2016), 1–16  mathnet  crossref  crossref  mathscinet  isi  elib
    210. G. D. Solomadin, Yu. M. Ustinovskiy, “Projective toric polynomial generators in the unitary cobordism ring”, Sb. Math., 207:11 (2016), 1601–1624  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    211. Wilfong A., “Toric polynomial generators of complex cobordism”, Algebr. Geom. Topol., 16:3 (2016), 1473–1491  crossref  mathscinet  zmath  isi  elib  scopus
    212. V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    213. Sabatini S., “On the Chern Numbers and the Hilbert Polynomial of An Almost Complex Manifold With a Circle Action”, Commun. Contemp. Math., 19:4 (2017), 1750043  crossref  isi
    214. Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59  crossref  isi
    215. Daniel M. Kane, Joseph Palmer, Álvaro Pelayo, “Classifying Toric and Semitoric Fans by Lifting Equations from $\mathrm{SL}_2({\mathbb Z})$”, SIGMA, 14 (2018), 016, 43 pp.  mathnet  crossref
    216. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    217. I. Yu. Limonchenko, T. E. Panov, G. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    218. V. V. Batyrev, K. Schaller, “Stringy $E$-functions of canonical toric Fano threefolds and their applications”, Izv. Math., 83:4 (2019), 676–697  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    219. Diaz R., Cano L., “Continous Analogues For the Binomial Coefficients and the Catalan Numbers”, Appl. Anal. Discret. Math., 13:2 (2019), 542–568  crossref  isi
    220. Hausen J., Hische Ch., Wrobel M., “On Torus Actions of Higher Complexity”, Forum Math. Sigma, 7 (2019), e38  crossref  isi
    221. K. Altmann, D. Ploog, “Displaying the cohomology of toric line bundles”, Izv. Math., 84:4 (2020), 683–693  mathnet  crossref  crossref  isi
    222. Sarkar S., Song J., “Gkm Theory For Orbifold Stratified Spaces and Application to Singular Toric Varieties”, Topology Appl., 288 (2021), 107472  crossref  isi
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