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Donaldson–Thomas theory of 𝒜n×P1
- Part of
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- Journal:
- Compositio Mathematica / Volume 145 / Issue 5 / September 2009
- Published online by Cambridge University Press:
- 18 August 2009, pp. 1249-1276
- Print publication:
- September 2009
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- Article
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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
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.
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