The possible values of geometric genera of normal surface singularities

2019/11/13 by Nagy, János
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.07300

Abstract

In this article we prove that the possible geometric genuses p_g(\tX) corresponding to normal surface singularities \tX with fixed negative definite resolution graph T form an interval of integers. Similarly let us have a resolution graph T and a fixed normal surface singularity (X, 0) with resolution \tX and resolution graph T, furthermore consider a Chern class l' ∈ L'. We prove that the possible values of h¹(\tX, \calL), where \calL ∈ \pic^l'(\tX) form an interval of integers.

Related

• Invariants of relatively generic structures on normal surface\n singularities
• Normal surface singularities of small degrees
• On surfaces of high degree with respect to the sectional genus
• Hyperelliptic involutions on generic normal surface singularities
• Singular elliptic genus of normal surfaces