Invariance of elliptic genus under wall-crossing

Henry Liu

Invariance of elliptic genus under wall-crossing

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arxiv 2405.12587 v1 pith:7B4E5RY4 submitted 2024-05-21 math.AG

Henry Liu This is my paper · ORCID

classification math.AG

keywords followingwall-crossingellipticformulasgenusapplicationscriteriondonaldson-thomas

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Wall-crossing formulas for various flavors of elliptic genus can be obtained using master spaces. We give a topological criterion which implies that such wall-crossing formulas are trivial. Applications are given for: GIT quotients, following Thaddeus; moduli of sheaves, following Mochizuki; Donaldson-Thomas and Vafa-Witten theory, following Joyce and Tanaka-Thomas respectively.

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Nonabelian shift operators and shifted Yangians
math.AG 2024-12 conditional novelty 6.0 of 10

New nonabelian shift operators and wall-crossing identities show that the quantized Coulomb branch of pure GL_n gauge theory is a quotient of the shifted Yangian Y_{-nα}(sl2), with vertex functions as Hecke eigenfunctions.

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