A FINITENESS THEOREM FOR DUAL GRAPHS OF SURFACE SINGULARITIES

Author:

POPESCU-PAMPU PATRICK1,SEADE JOSÉ2

Affiliation:

1. Université Paris 7 Denis Diderot, Institut de Mathématiques-UMR CNRS 7586, équipe "Géométrie et dynamique", Site Chevaleret, Case 7012, 75205 Paris Cedex 13, France

2. Unidad Cuernavaca del Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, México

Abstract

Consider a fixed connected, finite graph Γ and equip its vertices with weights pi which are non-negative integers. We show that there is a finite number of possibilities for the coefficients of the canonical cycle of a numerically Gorenstein surface singularity having Γ as the dual graph of the minimal resolution, the weights pi of the vertices being the arithmetic genera of the corresponding irreducible components. As a consequence we get that if Γ is not a cycle, then there is a finite number of possibilities of self-intersection numbers which one can attach to the vertices which are of valency ≥ 2, such that one gets the dual graph of the minimal resolution of a numerically Gorenstein surface singularity. Moreover, we describe precisely the situations when there exists an infinite number of possibilities for the self-intersections of the component corresponding to some fixed vertex of Γ.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Reference17 articles.

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Discriminant groups of wild cyclic quotient singularities;Algebra & Number Theory;2023-05-09

2. A note on 3-manifolds and complex surface singularities;Mathematische Zeitschrift;2019-03-12

3. Some Open Problems in Complex Singularities;Springer Proceedings in Mathematics & Statistics;2018

4. Numerically Gorenstein surface singularities are homeomorphic to Gorenstein ones;Duke Mathematical Journal;2011-09-15

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