Hyperbolicity of nodal hypersurfaces

Fedor Bogomolov; Bruno De Oliveira

doi:10.1515/CRELLE.2006.053

Hyperbolicity of nodal hypersurfaces

Fedor Bogomolov, Bruno De Oliveira

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a nodal hypersurface X in ³ of degree d with a sufficiently large number l of nodes, , is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families.

Original language	English (US)
Pages (from-to)	89-101
Number of pages	13
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	596
DOIs	https://doi.org/10.1515/CRELLE.2006.053
State	Published - Jul 1 2006

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2006.053

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title = "Hyperbolicity of nodal hypersurfaces",

abstract = "We show that a nodal hypersurface X in 3 of degree d with a sufficiently large number l of nodes, , is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families.",

author = "Fedor Bogomolov and {De Oliveira}, Bruno",

note = "Funding Information: 2) Partially supported by the NSF grant DMS-0306487. Funding Information: 1) Partially supported by the NSF grant DMS-0404715.",

year = "2006",

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doi = "10.1515/CRELLE.2006.053",

language = "English (US)",

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N2 - We show that a nodal hypersurface X in 3 of degree d with a sufficiently large number l of nodes, , is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families.

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Hyperbolicity of nodal hypersurfaces

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