NC-smooth algebroid thickenings for families of vector bundles and quiver representations

TL;DR

This paper constructs NC-smooth algebroid thickenings over specific smooth varieties, extending deformation quantization concepts to families of vector bundles and quiver representations.

Contribution

It introduces NC-smooth algebroid thickenings for two classes of smooth varieties, generalizing deformation quantization to these settings.

Findings

Construction of NC-smooth algebroid thickenings over vector bundle families

Construction of NC-smooth algebroid thickenings over quiver representation families

Extension of deformation quantization concepts to new geometric contexts

Abstract

In his work on deformation quantization of algebraic varieties Kontsevich introduced the notion of algebroid as a certain generalization of a sheaf of algebras. We construct algebroids which are given locally by NC-smooth thickenings in the sense of Kapranov, over two classes of smooth varieties: the bases of miniversal families of vector bundles on projective curves, and the bases of miniversal families of quiver representations.