Gromov–Witten theory of 𝒜n–resolutions

Maulik, Davesh¹

¹ Department of Mathematics, Columbia University, New York, NY 10027, USA

Geometry & topology, Tome 13 (2009) no. 3, pp. 1729-1773.

Résumé

We give a complete solution for the reduced Gromov–Witten theory of resolved surface singularities of type $A_n$, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the $T$–equivariant relative Gromov–Witten theory of the threefold ${\mathcal{A}}_n\times P^1$ 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 ${\mathcal{A}}_n$ 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 $P^1$.

Détail

DOI : 10.2140/gt.2009.13.1729

Keywords: Gromov–Witten theory, ADE singularity

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