General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Izv. RAN. Ser. Mat.:

Personal entry:
Save password
Forgotten password?

Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 925–945 (Mi izv1541)  

This article is cited in 37 scientific papers (total in 37 papers)

Newton polyhedra and an algorithm for computing Hodge–Deligne numbers

V. I. Danilov, A. G. Khovanskii

Abstract: An algorithm is given for computing the mixed Hodge structure (more precisely, the Hodge–Deligne numbers) for cohomology of complete intersections in toric varieties in terms of Newton polyhedra specifying the complete intersection. In some particular cases the algorithm leads to explicit formulas.
Bibliography: 8 titles.

Full text: PDF file (2241 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 279–298

Bibliographic databases:

UDC: 512.7
MSC: Primary 14F25, 14C30, 14L32; Secondary 32J25, 14J40, 52A25
Received: 13.07.1984

Citation: V. I. Danilov, A. G. Khovanskii, “Newton polyhedra and an algorithm for computing Hodge–Deligne numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 925–945; Math. USSR-Izv., 29:2 (1987), 279–298

Citation in format AMSBIB
\by V.~I.~Danilov, A.~G.~Khovanskii
\paper Newton polyhedra and an algorithm for computing Hodge--Deligne numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 5
\pages 925--945
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 279--298

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. G. M. Doorn, J. H. M. Steenbrink, “A supplement to the monodromy theorem”, Abh Math Semin Univ Hambg, 59:1 (1989), 225  crossref  mathscinet  zmath
    2. Riccardo Benedetti, Francois Loeser, Jean Jacques Risler, “Bounding the number of connected components of a real algebraic set”, Discrete Comput Geom, 6:1 (1991), 191  crossref  mathscinet  zmath
    3. Ben Lichtin, “Periods and the asymptotics of a diophantine problem: I”, Ark Mat, 30:1-2 (1992), 105  crossref  mathscinet  zmath  isi
    4. Lothar Göttsche, “Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces”, Math Z, 223:1 (1996), 247  crossref  mathscinet  zmath  isi
    5. A. Dimca, “Hodge numbers of hypersurfaces”, Abh Math Semin Univ Hambg, 66:1 (1996), 377  crossref  mathscinet  zmath
    6. Lothar Göttsche, “Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces”, Math Z, 223:2 (1996), 247  crossref
    7. Victor V Batyrev, Dimitrios I Dais, “Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry”, Topology, 35:4 (1996), 901  crossref
    8. J.M Rojas, “Toric intersection theory for affine root counting”, Journal of Pure and Applied Algebra, 136:1 (1999), 67  crossref
    9. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. A. D. Bruno, “Self-similar solutions and power geometry”, Russian Math. Surveys, 55:1 (2000), 1–42  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. J.Maurice Rojas, “Some Speed-Ups and Speed Limits for Real Algebraic Geometry”, Journal of Complexity, 16:3 (2000), 552  crossref
    12. Wei-ping Li, Zhenbo Qin, “On blowup formulae for the S-duality conjecture of Vafa and Witten III: relations with vertex operator algebras”, crll, 2002:542 (2002), 173  crossref  mathscinet  zmath
    13. E. N. Materov, “The Bott formula for toric varieties”, Mosc. Math. J., 2:1 (2002), 161–182  mathnet  mathscinet  zmath  elib
    14. Lev A. Borisov, Anvar R. Mavlyutov, “String cohomology of Calabi–Yau hypersurfaces via mirror symmetry”, Advances in Mathematics, 180:1 (2003), 355  crossref
    15. Maximilian Kreuzer, Erwin Riegler, David A. Sahakyan, “Toric complete intersections and weighted projective space”, Journal of Geometry and Physics, 46:2 (2003), 159  crossref
    16. A. L. KHOLODENKO, “NEW STRING AMPLITUDES FROM OLD FERMAT (HYPER)SURFACES”, Int. J. Mod. Phys. A, 19:11 (2004), 1655  crossref
    17. Albrecht Klemm, Maximilian Kreuzer, Erwin Riegler, Emanuel Scheidegger, “Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections”, J High Energy Phys, 2005:5 (2005), 023  crossref  mathscinet
    18. Benoit Bertrand, “Asymptotically Maximal Families of Hypersurfaces in Toric Varieties”, Geom Dedicata, 118:1 (2006), 49  crossref  mathscinet  zmath  isi
    19. Jae-Yoo Choy, Young-Hoon Kiem, “NONEXISTENCE OF A CREPANT RESOLUTION OF SOME MODULI SPACES OF SHEAVES ON A K3 SURFACE”, Journal of the Korean Mathematical Society, 44:1 (2007), 35  crossref  isi
    20. Jonathan A. Cox, “An Additive Basis for the Chow Ring of $\overline{\mathcal M}_{0,2}(\mathbb P^r,2)$”, SIGMA, 3 (2007), 085, 16 pp.  mathnet  crossref  mathscinet  zmath
    21. Przyjalkowski V., “On Landau-Ginzburg models for Fano varieties”, Communications in Number Theory and Physics, 1:4 (2007), 713–728  isi
    22. Anvar R Mavlyutov, “Cohomology of rational forms and a vanishing theorem on toric varieties”, crll, 2008:615 (2008), 45  crossref  mathscinet  zmath  isi
    23. Young-Hoon Kiem, Sang-Bum Yoo, “The stringy E-function of the moduli space of Higgs bundles with trivial determinant”, Math Nachr, 281:6 (2008), 817  crossref  mathscinet  zmath  isi
    24. Sławomir Rams, “Defect and Hodge numbers of hypersurfaces”, advg, 8:2 (2008), 257  crossref  mathscinet
    25. Vicente Muñoz, “Hodge polynomials of the moduli spaces of rank 3 pairs”, Geom Dedicata, 136:1 (2008), 17  crossref
    26. Benoit Bertrand, “Euler characteristic of primitive T-hypersurfaces and maximal surfaces”, JMJ, 2009, 1  crossref  isi
    27. E. Gorsky, “Adams operations and power structures”, Mosc. Math. J., 9:2 (2009), 305–323  mathnet  mathscinet  zmath
    28. S. M. Gusein-Zade, “Integration with respect to the Euler characteristic and its applications”, Russian Math. Surveys, 65:3 (2010), 399–432  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. N. A. Bushueva, “On isotopies and homologies of subvarieties of toric varieties”, Siberian Math. J., 51:5 (2010), 776–788  mathnet  crossref  mathscinet  isi
    30. Cristian González–Martínez, “The Hodge–Poincaré polynomial of the moduli spaces of stable vector bundles over an algebraic curve”, manuscripta math, 2011  crossref
    31. Corti A., Golyshev V., “Hypergeometric equations and weighted projective spaces”, Science China-Mathematics, 54:8 (2011), 1577–1590  crossref  isi
    32. A. Esterov, K. Takeuchi, “Motivic Milnor Fibers over Complete Intersection Varieties and their Virtual Betti Numbers”, International Mathematics Research Notices, 2011  crossref
    34. V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    35. 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
    36. A. G. Khovanskii, “Newton polytopes and irreducible components of complete intersections”, Izv. Math., 80:1 (2016), 263–284  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    37. S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:1463
    Full text:614
    First page:3

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019