On curves on sandwiched surface singularities

2007/01/23 by Jesús Fernández-Sánchez, Fernandez-Sanchez, Jesus
Computer Science · Mathematics · #13B22 #14H20 #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.math/0701641

openalex publication_date 2007/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in its local ring, the curves on the surface X obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these curves are obtained. New formulas for their multiplicity, intersection numbers and order of singularity at the singularities of X are given. The semigroup of branches going through a sandwiched singularity is effectively determined, too.

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