2010/01/08 by Eero Hyry, Hyry, Eero, Tarmo Järvilehto +1
Computer Science · Mathematics · #13H05 #14B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1001.1220
openalex publication_date 2010/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a two-dimensional regular local ring having an algebraically closed residue field and let a be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of a by means of the dual graph of the minimal log resolution of the pair (X,a). Our main result is a combinatorial criterium for a positive rational number to be a jumping number. In particular, we associate to each jumping number certain ordered tree structures on the dual graph.