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arXiv · 2012.05278

Refinements of Kool-Thomas Invariants via Equivariant $K$-theoretic invariants

Rizal Afgani
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Abstract

In this article we are defining a refinement of Kool-Thomas invariants of local surfaces via the equivariant $K$-theoretic invariants proposed by Nekrasov and Okounkov. Kool and Thomas defined the reduced obstruction theory for the moduli of stable pairs $\mathcal{P}_{\chi}(X,i_{*}\beta)$ as the degree of the virtual class $\left[\mathcal{P}_{\chi}(S,\beta)\right]^{red}$ after we apply $\tau([pt])^{m}\in H^{*}(\mathcal{P}_{\chi}(X,i_{*}\beta),\mathbb{Z})$. $\tau([pt])$ contain the information of the incidence of a point and a curve supporting a $(\mathcal{F},s)$. $\textbf{Keywords: }$Kool-Thomas invariants, $K$-theoretic invariants, G\"ottsche Shende invariants

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Rizal Afgani. 2020-12-09. Refinements of Kool-Thomas Invariants via Equivariant $K$-theoretic invariants. https://arxiv.org/abs/2012.05278

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