Classical deformations of noncompact surfaces and their moduli of instantons

Abstract

We describe semiuniversal deformation spaces for the noncompact surfaces $Z_k:=\mathrm{Tot}({\mathcal{O}}_{{\mathbb{P}}^1}(-k))$ 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.

15 pages

References in corpus (4)

• Lectures on deformations of complex manifolds
• Local moduli of holomorphic bundles
• Deformations of Noncompact Calabi-Yau threefolds
• Isomorphisms of Moduli Spaces

Cited by in corpus (4)

• Deformation-obstruction theory for diagrams of algebras and applications to geometry
• Deformations of path algebras of quivers with relations
• Poisson structures on the conifold and local Calabi-Yau threefolds
• Infinite dimensional families of Calabi-Yau threefolds and moduli of vector bundles