2006/02/25 by Wenliang Zhang, Zhang, Wenliang
Mathematics · #13D45 #14B15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #math.AC #math.AG #msc:13D45 #msc:14B15
paper · pdf · doi:10.48550/arxiv.math/0602566
arxiv created 2006/02/25 · openalex publication_date 2006/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a d-dimensional local ring containing a field. We will prove that the highest Lyubeznik number λd,d(A) (defined in \citel1) is equal to the number of connected components of the Hochster-Huneke graph (defined in \citehh) associated to B, where B=Ash is the completion of the strict Henselization of the completion of A. This was proven by Lyubeznik in characteristic p>0. Our statement and proof are characteristic-free.