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Node polynomials for families: methods and applications

✍ Scribed by Steven L. Kleiman; Ragni Piene

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
293 KB
Volume
271
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We continue the development of methods for enumerating nodal curves on smooth complex surfaces, extending the range of validity. We apply the new methods in three important cases. First, for up to eight nodes, we prove Göttsche's conjecture about plane curves of low degree. Second, we prove Vainsencher's conjectural enumeration of irreducible six‐nodal plane curves on a general quintic threefold in four‐space, which is important for Clemens' conjecture and mirror symmetry. Third, we supplement Bryan and Leung's enumeration of nodal curves in a given homology class on an Abelian surface of Picard number 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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