Stable maps and branch divisors
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 1999
 arXiv:
 arXiv:math/9905104
 Bibcode:
 1999math......5104F
 Keywords:

 Algebraic Geometry
 EPrint:
 21 pages, LaTex2e