The local Donaldson-Thomas theory of curves

2005/12/26 by Okounkov, A., Pandharipande, R. · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0512573

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.

Cited by

• The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants
• Donaldson-Thomas invariants of [\mathbb C⁴/\mathbb Z_r]

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