On multi-pointed non-commutative deformations and Calabi-Yau threefolds

TL;DR

This paper develops a theory of multi-pointed non-commutative deformations for simple collections in abelian categories, constructing relative exceptional and spherical objects, inspired by Donovan and Wemyss's work.

Contribution

It introduces a new framework for multi-pointed non-commutative deformations and constructs related exceptional and spherical objects in certain cases.

Findings

Established a theory of multi-pointed non-commutative deformations.

Constructed relative exceptional objects.

Constructed relative spherical objects.

Abstract

We shall develop a theory of multi-pointed non-commutative deformations of a simple collection in an abelian category, and construct relative exceptional objects and relative spherical objects in some cases. This is inspired by a work by Donovan and Wemyss.