Symbol calculus on a projective space

TL;DR

This paper develops a symbol calculus framework on projective schemes, utilizing holomorphic Poisson structures to create deformations of ring structures on projective spaces.

Contribution

It introduces a novel symbol calculus approach on projective schemes, leveraging holomorphic Poisson structures for ring deformation.

Findings

Constructed deformations of ring structures on projective spaces.

Established a new symbol calculus framework for projective schemes.

Demonstrated applications of holomorphic Poisson structures in deformation theory.

Abstract

In this article, we introduce symbol calculus on a projective scheme. Using holomorphic Poisson structures, we construct deformations of ring structures for structure sheaves on projective spaces.