The construction problem for hodge numbers modulo an integer

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Matthias Paulsen
  • Stefan Schreieder

Externe Organisationen

  • Ludwig-Maximilians-Universität München (LMU)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)2427-2434
Seitenumfang8
FachzeitschriftAlgebra and Number Theory
Jahrgang13
Ausgabenummer10
PublikationsstatusVeröffentlicht - 2019
Extern publiziertJa

Abstract

For any integer m ≥ 2 and any dimension n ≥ 1, we show that any n-dimensional Hodge diamond with values in (FORMULA PRESENTED) is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Kollár in 2012.

ASJC Scopus Sachgebiete

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The construction problem for hodge numbers modulo an integer. / Paulsen, Matthias; Schreieder, Stefan.
in: Algebra and Number Theory, Jahrgang 13, Nr. 10, 2019, S. 2427-2434.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Paulsen M, Schreieder S. The construction problem for hodge numbers modulo an integer. Algebra and Number Theory. 2019;13(10):2427-2434. doi: 10.2140/ant.2019.13.2427
Paulsen, Matthias ; Schreieder, Stefan. / The construction problem for hodge numbers modulo an integer. in: Algebra and Number Theory. 2019 ; Jahrgang 13, Nr. 10. S. 2427-2434.
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abstract = "For any integer m ≥ 2 and any dimension n ≥ 1, we show that any n-dimensional Hodge diamond with values in (FORMULA PRESENTED) is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Koll{\'a}r in 2012.",
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N1 - Funding information: The second named author thanks J. Kollár and D. Kotschick for independently making him aware of Kollár’s question (answered in Corollary 3 above), which was the starting point of this paper. The authors are grateful to the referees for useful suggestions. This work is supported by the DFG project “Topologische Eigenschaften von algebraischen Varietäten” (project no. 416054549).

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