2023/09/08 by Ilya Smirnov, Smirnov, Ilya
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2309.04322
openalex publication_date 2023/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note grew from the lectures I delivered at ICTP during the Summer School in honor of Hochster and Huneke. Its purpose is to provide an introduction to the notion of equimultiplicity (of numerical invariants of singularities/local rings) and survey past work on equimultiplicity of Hilbert-Kunz multiplicity and F-signature. The treatment of F-signature is from joint work with Thomas Polstra and the section on Hilbert-Kunz multiplicity updates my previous paper on the topic and gives novel applications.