Quantizations of local surfaces and rebel instantons

Abstract

We construct explicit deformation quantizations of the noncompact complex surfaces $Z_k:=\mathrm{Tot}({\mathcal{O}}_{{\mathbb{P}}^1}(-k))$ and describe their effect on moduli spaces of vector bundles and instanton moduli spaces. We introduce the concept of rebel instantons, as being those which react badly to some quantizations, misbehaving by shooting off extra families of noncommutative instantons. We then show that the quantum instanton moduli space can be viewed as the étale space of a constructible sheaf over the classical instanton moduli space with support on rebel instantons.

38 pages, final version to appear in Journal of Noncommutative Geometry

References in corpus (4)

• Multiple zeta values in deformation quantization
• Local moduli of holomorphic bundles
• The ADHM Construction of Instantons on Noncommutative Spaces
• Deformation-obstruction theory for diagrams of algebras and applications to geometry

Cited by in corpus (6)

• 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
• Deformations of categories of coherent sheaves via quivers with relations
• Deformations of noncompact Calabi--Yau manifolds, families and diamonds