Hyperbolicity of nodal hypersurfaces

Fedor Bogomolov, Bruno De Oliveira

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)89-101
Number of pages13
JournalJournal fur die Reine und Angewandte Mathematik
Issue number596
DOIs
StatePublished - Jul 1 2006

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Hyperbolicity
Hypersurface
Rational Curves
Foliation
Elliptic Curves
Vertex of a graph
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hyperbolicity of nodal hypersurfaces. / Bogomolov, Fedor; De Oliveira, Bruno.

In: Journal fur die Reine und Angewandte Mathematik, No. 596, 01.07.2006, p. 89-101.

Research output: Contribution to journalArticle

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