dc.contributor.author Némethi A. en_US dc.contributor.author Nagy J. en_US dc.date.accessioned 2020-10-08T15:20:27Z dc.date.available 2020-10-08T15:20:27Z dc.date.issued 2019 dc.identifier.issn 0025-5831 dc.identifier.uri http://hdl.handle.net/20.500.11824/1158 dc.description.abstract Abstract. Let (X, o) be a complex normal surface singularity. We fix one of its good resolutions X → X, an effective cycle Z supported on the reduced exceptional curve, and any possible (first Chern) class l′ ∈ H 2 (X , Z). With these data we define the variety ECal′ (Z ) of those effective Cartier divisors D supported on Z which determine a line bundles OZ (D) with first Chern class l′. Furthermore, we consider the affine space Picl′ (Z) ⊂ H1(OZ∗ ) of isomorphism classes of holomorphic line bundles with Chern class l′ and the Abel map cl′ (Z) : ECal′ (Z) → Picl′ (Z). The present manuscript develops the major properties of this map, and links them with the determination of the cohomology groups H1(Z,L), where we might vary the analytic structure (X, o) (supported on a fixed topological type/resolution graph) and we also vary the possible line bundles L ∈ Picl′ (Z). The case of generic line bundles of Picl′ (Z) and generic line bundles of the image of the Abel map will have priority roles. Rewriting the Abel map via Laufer duality based on integration of forms on divisors, we can make explicit the Abel map and its tangent map. The case of superisolated and weighted homogeneous singularities are exemplified with several details. en_US The theory has similar goals (but rather different techniques) as the theory of Abel map or Brill–Noether theory of reduced smooth projective curves. dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Mathematische Annalen en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject weighted homogeneous singularity. en_US dc.subject superisolated singularity en_US dc.subject splice quotient singularity en_US dc.subject surgery formulae en_US dc.subject Laufer duality en_US dc.subject Brill–Noether theory en_US dc.subject Picard group en_US dc.subject effective Cartier divisor en_US dc.subject Abel map en_US dc.subject normal surface singularity en_US dc.subject resolution graph en_US dc.subject rational homology sphere en_US dc.subject natural line bundle en_US dc.subject Poincar ́e series en_US dc.title The Abel map for surface singularities I. Generalities and examples en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/publishedVersion en_US dc.identifier.doi 10.1007/s00208-019-01873-w dc.relation.publisherversion https://link.springer.com/article/10.1007/s00208-019-01873-w en_US
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