Rank 2 parabolic bundles and generalized theta functions
type: Item
instance of: scholarly article
title: Rank 2 parabolic bundles and generalized theta functions
zbMATH Open document ID: 0905.14016
DOI: 10.1007/PL00004601
author: Christian Pauly
published in: Mathematische Zeitschrift
publication date: 1998-08-09T00:00:00Z
review text: Let \({\mathcal N}= {\mathcal N} (k,\vec d)\) be the moduli space of rank 2 semi-stable parabolic vector bundles with fixed trivial determinant over a smooth projective curve \(C\). We determine the Picard group of \({\mathcal N}\) and define Cartier divisors in the linear system \(| {\mathfrak L}^{\text{par}} |\), where \({\mathfrak L}^{\text{par}}\) is an ample determinant line bundle over \({\mathcal N}\). If \(k=2\) and \(d_i=1\), we show an isomorphism between the space of global sections \(H^0 ({\mathcal N}, {\mathfrak L}^{\text{par}})\) and a direct sum of spaces of theta functions of order 4 over the Jacobian of \(C\).
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14M12
zbMATH DE Number: 1185891
zbMATH Keywords: moduli space of rank 2 semi-stable parabolic vector bundles
zbMATH Keywords: Picard group
zbMATH Keywords: Cartier divisors
zbMATH Keywords: determinant line bundle
zbMATH Keywords: theta functions
zbMATH Keywords: Jacobian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1185891