A variant of the Mukai pairing via deformation quantization

TL;DR

This paper introduces a novel approach to computing a variant of the Mukai pairing using deformation quantization, leveraging advanced results in the field to potentially extend to singular varieties.

Contribution

It presents a new proof method for a Mukai pairing variant based on deformation quantization and related algebraic index theorems.

Findings

New proof technique for Mukai pairing variant

Utilizes deformation quantization and algebraic index theorems

Potential for generalization to singular varieties

Abstract

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.