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.

21 pages, LaTex2e

References in corpus (3)

• Quantum Cohomology and Virasoro Algebra
• Virasoro constraints and the Chern classes of the Hodge bundle
• Recursions, formulas, and graph-theoretic interpretations of ramified coverings of the sphere by surfaces of genus 0 and 1

Cited by in corpus (8)

• Hurwitz numbers and intersections on moduli spaces of curves
• BPS states of curves in Calabi--Yau 3--folds
• Hodge integrals and Hurwitz numbers via virtual localization
• The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals
• Gromov-Witten invariants of Fano threefolds of genera 6 and 8
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
• The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals
• Open ${\mathbb{CP}}^1$ descendent theory I: The stationary sector