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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)
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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
\Bibitem{DanKho86}
\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
\mathnet{http://mi.mathnet.ru/izv1541}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=873655}
\zmath{https://zbmath.org/?q=an:0669.14012}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 279--298
\crossref{https://doi.org/10.1070/IM1987v029n02ABEH000970}


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    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
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    14. Lev A. Borisov, Anvar R. Mavlyutov, “String cohomology of Calabi–Yau hypersurfaces via mirror symmetry”, Advances in Mathematics, 180:1 (2003), 355  crossref
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    16. A. L. KHOLODENKO, “NEW STRING AMPLITUDES FROM OLD FERMAT (HYPER)SURFACES”, Int. J. Mod. Phys. A, 19:11 (2004), 1655  crossref
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    18. Benoit Bertrand, “Asymptotically Maximal Families of Hypersurfaces in Toric Varieties”, Geom Dedicata, 118:1 (2006), 49  crossref  mathscinet  zmath  isi
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    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
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    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
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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