Donaldson-Thomas theory of A_n x P^1

Details Donaldson-Thomas theory of A_n x P^1 Donaldson-Thomas theory of A_n x P^1

2008-02-20

arxiv.org/abs/0802.2739v3

Mathematics

Algebraic Geometry

30 pages, 2 figures; minor changes

Scientific paper

We study the relative Donaldson-Thomas theory of A_n x P^1, where A_n is the surface resolution of a type A_n singularity. The action of divisor operators in the theory is expressed in terms of operators of the affine algebra \hat{gl}(n+1) on Fock space. Assuming a nondegeneracy conjecture, this gives a complete solution for the theory. The results complete the comparison of this theory with the Gromov-Witten theory of A_n x P^1 and the quantum cohomology of the Hilbert scheme of points on A_n.

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