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Uspekhi Mat. Nauk, 1999, Volume 54, Issue 2(326), Pages 113–162 (Mi umn134)  

This article is cited in 25 scientific papers (total in 25 papers)

An analogue of the Hodge–Riemann relations for simple convex polytopes

V. A. Timorin

Independent University of Moscow

DOI: https://doi.org/10.4213/rm134

Full text: PDF file (445 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1999, 54:2, 381–426

Bibliographic databases:

UDC: 514.172.45+514.177+515.165.4
MSC: 52B05, 14M25, 52B20
Received: 08.02.1999

Citation: V. A. Timorin, “An analogue of the Hodge–Riemann relations for simple convex polytopes”, Uspekhi Mat. Nauk, 54:2(326) (1999), 113–162; Russian Math. Surveys, 54:2 (1999), 381–426

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. V. M. Buchstaber, T. E. Panov, “Torus actions, combinatorial topology, and homological algebra”, Russian Math. Surveys, 55:5 (2000), 825–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. A. Timorin, “On Polytopes that are Simple at the Edges”, Funct. Anal. Appl., 35:3 (2001), 189–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. B. Ya. Kazarnovskii, “c-fans and Newton polyhedra of algebraic varieties”, Izv. Math., 67:3 (2003), 439–460  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Stanley R.P., “Recent developments in algebraic combinatorics”, Israel J. Math., 143:1 (2004), 317–339  crossref  mathscinet  zmath  isi  elib  scopus
    5. Karu K., “Hard Lefschetz theorem for nonrational polytopes”, Invent. Math., 157:2 (2004), 419–447  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Kaveh, K, “Vector fields and the cohomology ring of toric varieties”, Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques, 48:3 (2005), 414  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Bressler, P, “Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes”, Indiana University Mathematics Journal, 54:1 (2005), 263  crossref  mathscinet  zmath  isi  scopus
    8. Braden, T, “Remarks on the combinatorial intersection cohomology of fans”, Pure and Applied Mathematics Quarterly, 2:4 (2006), 1149  crossref  mathscinet  zmath  isi
    9. Bosio, F, “Real quadrics in C-n, complex manifolds and convex polytopes”, Acta Mathematica, 197:1 (2006), 53  crossref  mathscinet  zmath  isi  elib  scopus
    10. Barthel G., Kaup L., Brasselet J.-P., Fieseler K.-H., “Hodge-Riemann relations for polytopes a geometric approach”, Singularity Theory, 2007, 379–410  crossref  mathscinet  zmath  adsnasa  isi
    11. Cattani, E, “Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations”, International Mathematics Research Notices, 2008, rnn025  crossref  mathscinet  zmath  isi  scopus
    12. Meersseman L., Verjovsky A., “LV-M varieties”, Singularities II: Geometric and Topological Aspects, Contemporary Mathematics Series, 475, 2008, 111–134  crossref  mathscinet  zmath  isi
    13. Braden T., Licata A., Proudfoot N., Webster B., “Gale duality and Koszul duality”, Advances in Mathematics, 225:4 (2010), 2002–2049  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Fleming B., Karu K., “Hard Lefschetz theorem for simple polytopes”, Journal of Algebraic Combinatorics, 32:2 (2010), 227–239  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. McDuff D., Tolman S., “Polytopes with Mass Linear Functions, Part 1”, International Mathematics Research Notices, 2010, no. 8, 1506–1574  mathscinet  zmath  isi  elib
    16. Dusa McDuff, “The topology of toric symplectic manifolds”, Geom. Topol, 15:1 (2011), 145  crossref  mathscinet  zmath  isi  scopus  scopus
    17. 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
    18. Kaveh K., “Note on Cohomology Rings of Spherical Varieties and Volume Polynomial”, J Lie Theory, 21:2 (2011), 263–283  mathscinet  zmath  isi  elib
    19. D. McDuff, S. Tolman, “Polytopes with Mass Linear Functions II: The Four-Dimensional Case”, International Mathematics Research Notices, 2012  crossref  mathscinet  isi  scopus  scopus
    20. V. A. Kirichenko, E. Yu. Smirnov, V. A. Timorin, “Schubert calculus and Gelfand–Zetlin polytopes”, Russian Math. Surveys, 67:4 (2012), 685–719  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    21. Zak F.L., “Castelnuovo Bounds for Higher-Dimensional Varieties”, Compos. Math., 148:4 (2012), 1085–1132  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    22. Askold Khovanskiǐ, Vladlen Timorin, “On the Theory of Coconvex Bodies”, Discrete Comput Geom, 2014  crossref  mathscinet  isi  scopus  scopus
    23. F. Battaglia, D. Zaffran, “Foliations Modeling Nonrational Simplicial Toric Varieties”, International Mathematics Research Notices, 2015  crossref  mathscinet  isi  scopus  scopus
    24. G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. Grigory D. Solomadin, “Quasitoric totally normally split manifolds”, Proc. Steklov Inst. Math., 302 (2018), 358–379  mathnet  crossref  crossref  mathscinet  isi  elib
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