Noncommutative varieties and stability conditions: an overview

TL;DR

This paper surveys recent advances in noncommutative algebraic geometry, focusing on stability conditions and moduli spaces, and explores their applications in hyperk"ahler and classical algebraic geometry.

Contribution

It provides an overview of recent progress connecting noncommutative varieties with stability conditions and moduli spaces, highlighting new developments and applications.

Findings

Enhanced understanding of stability conditions in noncommutative geometry

New connections between noncommutative varieties and hyperk"ahler geometry

Progress in moduli space theory within noncommutative algebraic geometry

Abstract

Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.