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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2006, Issue 596


Hyperbolicity of nodal hypersurfaces

Fedor Bogomolov / Bruno De Oliveira
Published Online: 2006-08-16 | DOI: https://doi.org/10.1515/CRELLE.2006.053


We show that a nodal hypersurface X in ℙ3 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.

About the article

Received: 2004-11-02

Revised: 2005-03-05

Published Online: 2006-08-16

Published in Print: 2006-07-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2006, Issue 596, Pages 89–101, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.053.

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