The geometric genus of splice-quotient singularities

Okuma, Tomohiro

doi:10.1090/S0002-9947-08-04559-5

The geometric genus of splice-quotient singularities
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Trans. Amer. Math. Soc. 360 (2008), 6643-6659 Request permission

Abstract:

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.

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