The cohomology of line bundles of splice-quotient singularities
By A. N'emethi. 2008
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Abstract We provide several results on splice-quotient singularities: (1) a combinatorial expression of the dimension of the first cohomology of all ‘natural’ line bundles (involving the Seiberg–Witten invariants of the singularity link); (2) an equivariant Campillo–Delgado–Gusein-Zade type formula about the dimension of relative sections of line bundles, extending former results about rational and minimally elliptic singularities; (3) in particular, we prove that the equivariant, divisorial multi-variable Hilbert–Poincare series is topological; (4) a combinatorial description of divisors of analytic function-germs; (5) and an expression for the multiplicity of the singularity from its resolution graph (in particular solving Zariskiʼs Multiplicity Conjecture for splice-quotient hypersurfaces). From topological point of view, we get a new combinatorial expression for the Seiberg–Witten invariants of links of splice-quotient singularities.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a8fe7d519f0cdde98e2c4a07bb96d4fbe439de82
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Seiberg-Witten invariants of negative definite plumbed 3-manifolds (2010, methodology): “ne has Theorem B. For any Γ and σ as above −eu(H∗(Γ,σ)) = sw σ(M(Γ)). In fact, Theorem A was motivated by a similar formula valid for equivariant geometric genera of normal surface singularities, cf. [N08c]; this is explained in (2.2). The combinatorial quadratic Hilbert-polynomial type behaviour (1”