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Stable Maps and Branch Divisors

Fantechi, B. and Pandharipande, R. (2002) Stable Maps and Branch Divisors. Compositio Mathematica, 130 (3). pp. 345-364. ISSN 0010-437X. doi:10.1023/A:1014347115.

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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 construction 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 the projective line for all genera and degrees in terms of Hodge integrals.

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Additional Information:© 2002 Kluwer Academic Publishers. Received: 10 July 2000. We thank T. Graber and R. Vakil for many discussions about Hurwitz numbers. The authors thank the Mittag-Leffler Institute where this research was partially carried out. The second author was partially supported by National Science Foundation grant DMS-9801574.
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Subject Keywords:branch divisor; Hurwitz number
Issue or Number:3
Record Number:CaltechAUTHORS:20111019-093513416
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Official Citation:Fantechi, B. & Pandharipande, R. Compositio Mathematica (2002) 130: 345.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27300
Deposited By: Tony Diaz
Deposited On:25 Oct 2011 15:05
Last Modified:09 Nov 2021 16:47

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