Title

Spin Hurwitz numbers and the Gromov-Witten invariants of Kahler surfaces

Authors

Authors

J. Lee;T. H. Parker

Comments

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Abbreviated Journal Title

J. Eng. Mech.-ASCE

Keywords

Mathematics

Abstract

The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These "spin Hurwitz numbers," recently studied by Eskin, Okounkov and Pandharipande, are interesting in their own right. By the authors' previous work, they are also related to the Gromov-Witten invariants of Kahler surfaces. We prove a recursive formula for spin Hurwitz numbers, which then gives the dimension zero GW invariants of Kahler surfaces with positive geometric genus. The proof uses a degeneration of spin curves, an invariant defined by the spectral flow of certain anti-linear deformations of (partial derivative) over bar and an interesting localization phenomenon for eigenfunctions that shows that maps with even ramification points cancel in pairs.

Journal Title

Communications in Analysis and Geometry

Volume

Commun. Anal. Geom.

Issue/Number

5

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

1015

Last Page

1060

WOS Identifier

21

ISSN

1019-8385

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