Spherical subcategories in algebraic geometry

TL;DR

This paper investigates spherical objects in triangulated categories, establishing a unique maximal subcategory where these objects are spherical, and applies this framework to algebraic geometry contexts.

Contribution

It introduces a general theory for spherical objects in triangulated categories and identifies a unique maximal subcategory for their spherical property, with applications in algebraic geometry.

Findings

Existence of a unique maximal triangulated subcategory for spherical objects.

Application of the theory to algebraic geometry.

Framework for studying spherical objects in various contexts.

Abstract

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general result is then applied to algebraic geometry.