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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 61–68 (Mi mz3767)  

This article is cited in 4 scientific papers (total in 4 papers)

A Remark on the Nonrationality Problem for Generic Cubic Fourfolds

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is proved that the nonrationality of a generic cubic fourfold follows from a conjecture on the nondecomposability in the direct sum of nontrivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on a projective surface.

Keywords: nonrationality problem, generic cubic fourfold, nondecomposability conjecture, polarized Hodge structure, projective surface

DOI: https://doi.org/10.4213/mzm3767

Full text: PDF file (498 kB)
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English version:
Mathematical Notes, 2008, 83:1, 57–64

Bibliographic databases:

Document Type: Article
UDC: 517.956.32
Received: 31.10.2006

Citation: Vik. S. Kulikov, “A Remark on the Nonrationality Problem for Generic Cubic Fourfolds”, Mat. Zametki, 83:1 (2008), 61–68; Math. Notes, 83:1 (2008), 57–64

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Przyjalkowski V., Shramov C., “on Hodge Numbers of Complete Intersections and Landau-Ginzburg Models”, Int. Math. Res. Notices, 2015, no. 21, 11302–11332  crossref  mathscinet  zmath  isi  scopus
    2. Shen M., “Hyperkahler Manifolds of Jacobian Type”, J. Reine Angew. Math., 712 (2016), 189–223  crossref  mathscinet  zmath  isi  scopus
    3. Hassett B., “Cubic Fourfolds, K3 Surfaces, and Rationality Questions”, Rationality Problems in Algebraic Geometry, Lect. Notes Math., Lecture Notes in Mathematics, 2172, eds. Pardini R., Pirola G., Springer International Publishing Ag, 2016, 29–66  crossref  mathscinet  isi  scopus
    4. Auel A. Bernardara M., “Cycles, Derived Categories, and Rationality”, Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 95, ed. Coskun I. DeFernex T. Gibney A., Amer Mathematical Soc, 2017, 199–266  crossref  mathscinet  zmath  isi  scopus
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