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2020 Degeneracy loci, virtual cycles and nested Hilbert schemes, I
Amin Gholampour, Richard P. Thomas
Tunisian J. Math. 2(3): 633-665 (2020). DOI: 10.2140/tunis.2020.2.633

Abstract

Given a map of vector bundles on a smooth variety, consider the deepest degeneracy locus where its rank is smallest. We show it carries a natural perfect obstruction theory whose virtual cycle can be calculated by the Thom–Porteous formula.

We show nested Hilbert schemes of points on surfaces can be expressed as degeneracy loci. We show how to modify the resulting obstruction theories to recover the virtual cycles of Vafa–Witten and reduced local DT theories. The result computes some Vafa–Witten invariants in terms of Carlsson–Okounkov operators. This proves and extends a conjecture of Gholampour, Sheshmani, and Yau and generalises a vanishing result of Carlsson and Okounkov.

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Amin Gholampour. Richard P. Thomas. "Degeneracy loci, virtual cycles and nested Hilbert schemes, I." Tunisian J. Math. 2 (3) 633 - 665, 2020. https://doi.org/10.2140/tunis.2020.2.633

Information

Received: 11 February 2019; Accepted: 20 June 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159378
MathSciNet: MR4041285
Digital Object Identifier: 10.2140/tunis.2020.2.633

Subjects:
Primary: 14D20, 14J60, 14N35
Secondary: 14C05, 57R57

Rights: Copyright © 2020 Mathematical Sciences Publishers

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