On moduli of Fano varieties: an introduction to K-stability and K-moduli

TL;DR

This survey introduces graduate students to the concepts of K-stability and K-moduli in algebraic geometry, providing foundational background for research on explicit K-moduli problems.

Contribution

It offers an accessible introduction to K-stability and K-moduli, bridging foundational knowledge and research applications for graduate students.

Findings

Provides essential background for K-moduli research

Clarifies the role of K-stability in algebraic geometry

Prepares students for explicit K-moduli problem investigations

Abstract

This survey article is an accompaniment to the 2025 Summer Research Institute in Algebraic Geometry Bootcamp on K-stability and K-moduli. It is aimed at graduate students and intended to provide the necessary background to begin research on explicit K-moduli problems.