Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten theories
Artan Sheshmani
TL;DR
This paper summarizes recent research connecting the enumerative geometry of nested Hilbert schemes on algebraic surfaces to threefold theories, highlighting their relations to Donaldson-Thomas, Vafa-Witten, and Seiberg-Witten theories.
Contribution
It consolidates and reviews the connections between nested Hilbert schemes and threefold theories, emphasizing their roles in modern enumerative geometry and mathematical physics.
Findings
Established links between nested Hilbert schemes and threefold theories
Clarified the role of Donaldson-Thomas, Vafa-Witten, and Seiberg-Witten theories in enumerative geometry
Summarized key results from arXiv:1701.08899 and arXiv:1701.08902
Abstract
This article provides a summary of arXiv:1701.08899 and arXiv:1701.08902 where the authors studied the enumerative geometry of nested Hilbert schemes of points and curves on algebraic surfaces and their connections to threefold theories, and in particular relevant Donaldson-Thomas, Vafa-Witten and Seiberg-Witten theories.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Algebra and Geometry