The local Donaldson-Thomas theory of curves
A. Okounkov, R. Pandharipande
TL;DR
This paper solves the local Donaldson-Thomas theory of curves using localization and degeneration, establishing deep connections with Gromov-Witten theory, quantum cohomology, and the Hilbert scheme of points of the plane.
Contribution
It completes a triangle of equivalences linking Donaldson-Thomas theory, Gromov-Witten theory, and quantum cohomology for curves.
Findings
Established the local Donaldson-Thomas theory of curves.
Connected the quantum differential equation of the Hilbert scheme to Donaldson-Thomas theory.
Determined the 1-legged equivariant vertex.
Abstract
The local Donaldson-Thomas theory of curves is solved by localization and degeneration methods. The results complete a triangle of equivalences relating Gromov-Witten theory, Donaldson-Thomas theory, and the quantum cohomology of the Hilbert scheme of points of the plane. The quantum differential equation of the Hilbert scheme of points of the plane has a natural interpretation in the local Donaldson-Thomas theory of curves. The solution determines the 1-legged equivariant vertex.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications