Donaldson–Thomas theory of 𝒜n×P1

Abstract We study the relative Donaldson–Thomas theory of 𝒜n×P1, where 𝒜n is the surface resolution of type An singularity. The action of divisor operators in the theory is expressed in terms of operators of the affine algebra $\glh $ 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 𝒜n×P1 and the quantum cohomology of the Hilbert scheme of points on 𝒜n.

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