Nagy, János and Némethi, András (2022) The dimension of the image of the Abel map associated with normal surface singularities. SELECTA MATHEMATICA  NEW SERIES, 28 (3). ISSN 10221824

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Abstract
Let (X,o) be a complex normal surface singularity with rational homology sphere link and let X˜ be one of its good resolutions. Fix an effective cycle Z supported on the exceptional curve and also a possible Chern class l′∈H2(X˜,Z). Define Ecal′(Z) as the space of effective Cartier divisors on Z and cl′(Z):Ecal′(Z)→Picl′(Z), the corresponding Abel map. In this note we provide two algorithms, which provide the dimension of the image of the Abel map. Usually, dimPicl′(Z)=pg, dimIm(cl′(Z)) and codimIm(cl′(Z)) are not topological, they are in subtle relationship with cohomologies of certain line bundles. However, we provide combinatorial formulae for them whenever the analytic structure on X˜ is generic. The codimIm(cl′(Z)) is related with {h1(X˜,L)}L∈Im(cl′(Z)); in order to treat the `twisted' family {h1(X˜,L0⊗L)}L∈Im(cl′(Z)) we need to elaborate a generalization of the Picard group and of the Abel map. The above algorithms are also generalized.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  07 Nov 2022 08:34 
Last Modified:  07 Nov 2022 08:34 
URI:  http://real.mtak.hu/id/eprint/152990 
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