Volume 13, issue 3 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Gromov–Witten theory of $\mathcal{A}_{n}$–resolutions

Davesh Maulik

Geometry & Topology 13 (2009) 1729–1773
Abstract

We give a complete solution for the reduced Gromov–Witten theory of resolved surface singularities of type An, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the T–equivariant relative Gromov–Witten theory of the threefold An ×P1 which, under a nondegeneracy hypothesis, yields a complete solution for the theory. The results given here allow comparison of this theory with the quantum cohomology of the Hilbert scheme of points on the An surfaces. We discuss generalizations to linear Hodge insertions and to surface resolutions of type D,E. As a corollary, we present a new derivation of the stationary Gromov–Witten theory of P1.

Keywords
Gromov–Witten theory, ADE singularity
Mathematical Subject Classification 2000
Primary: 14N35
References
Publication
Received: 5 March 2008
Revised: 10 December 2008
Accepted: 12 February 2009
Published: 5 March 2009
Proposed: Jim Bryan
Seconded: Yasha Eliashberg, Lothar Goettsche
Authors
Davesh Maulik
Department of Mathematics
Columbia University
New York, NY 10027
USA