Invariants of relatively generic structures on normal surface\n singularities

2019/10/08 by János Nagy, Nagy, János
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.03275

openalex publication_date 2019/10/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In the present article we work out a relative setup of generic structures on\nsurface singularities. We fix an analytic type on a subgraph of a rational\nhomology sphere resolution graph \T and we choose a relatively\ngeneric normal surface singularity tX with resolution graph \T.\nWe provide formulae for the geometric genus and the analytical Poincar 'e\nseries of tX. We determine the base point structure of natural line bundles\non tX and give a lower bound on the multiplicity of tX which is expected\nto be sharp. We prove similar results about cohomology numbers of relatively\ngeneric line bundles on every singularity with rational homology sphere link.\n

Citations

• Rees algebras and p_g-ideals in a two-dimensional normal local domain
• Good ideals and p_g-ideals in two-dimensional normal singularities

Related

• Base points of natural line bundles on relatively generic surface singularities
• Cohomology of natural line bundles on generic normal surface singularities
• The Abel map for surface singularities II. Generic analytic structure
• Invariants of relatively generic surface singularities II. Images of\n Abel maps
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