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Donaldson-Thomas theory of A_n x P^1

By D. Maulik and A. Oblomkov


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.Comment: 30 pages, 2 figures; minor change

Topics: Mathematics - Algebraic Geometry, Mathematics - Representation Theory
Year: 2008
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