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arXiv · 1604.01133

Classical deformations of noncompact surfaces and their moduli of instantons

Severin Barmeier·Elizabeth Gasparim
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Abstract

We describe semiuniversal deformation spaces for the noncompact surfaces $Z_k := \operatorname{Tot} (\mathcal O_{\mathbb P^1} (-k))$ and prove that any nontrivial deformation $Z_k (\tau)$ of $Z_k$ is affine. It is known that the moduli spaces of instantons of charge $j$ on $Z_k$ are quasi-projective varieties of dimension $2j-k-2$. In contrast, our results imply that the moduli spaces of instantons on any nontrivial deformation $Z_k (\tau)$ are empty.

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Severin Barmeier, Elizabeth Gasparim. 2016-04-05. Classical deformations of noncompact surfaces and their moduli of instantons. https://doi.org/10.1016/j.jpaa.2018.09.006

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