The space of curvettes of quotient singularities and associated\n invariants

2015/03/09 by José Agustín, Cogolludo-Agustin, Jose I., Jorge Martín-Morales +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1503.02487

openalex publication_date 2015/03/09 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

Abstract

This paper deals with a complete invariant R_X for cyclic quotient surface\nsingularities. This invariant appears in the Riemann Roch and Numerical\nAdjunction Formulas for normal surface singularities. Our goal is to give an\nexplicit formula for R_X based on the numerical information of X, that is,\nd and q as in X=X(d;1,q). In the process, the space of curvettes and\ngeneric curves is explicitly described. We also define and describe other\ninvariants of curves in X such as the LR-logarithmic eigenmodules,\n\δ-invariants, and their Milnor and Newton numbers.\n

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