Stable maps and branch divisors

B. Fantechi; R. Pandharipande

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arXiv · math/9905104

Stable maps and branch divisors

B. Fantechi·R. Pandharipande

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Abstract

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.

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BibTeX RIS

B. Fantechi, R. Pandharipande. 1999-05-18. Stable maps and branch divisors. https://arxiv.org/abs/math/9905104

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