Stable maps and branch divisors

We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor contruction of Mumford from sheaves to complexes. The construction is valid in flat families. The generalize...

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Bibliographic Details
Published in:arXiv.org 1999-05
Main Authors: Fantechi, B, Pandharipande, R
Format: Article
Language:English
Subjects:
Sheaves
Singularities
Online Access:Get full text
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Summary:We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor contruction of Mumford from sheaves to complexes. The construction is valid in flat families. The generalized branch divisor of a stable map to a nonsingular curve X yields a canonical morphism from the space of stable maps to a symmetric product of X. This branch morphism (together with virtual localization) is used to compute the Hurwitz numbers of covers of P^1 for all genera and degrees in terms of Hodge integrals.
ISSN:2331-8422