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Vector Bundles on Curves with Many Components
Author(s) -
Bhosle Usha N.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599011855
Subject(s) - mathematics , moduli space , vector bundle , euler characteristic , pure mathematics , projective variety , gravitational singularity , rank (graph theory) , disjoint sets , disjoint union (topology) , mathematical analysis , moduli , mathematics subject classification , torsion (gastropod) , combinatorics , medicine , physics , surgery , quantum mechanics
We construct the moduli spaces M ( n ) of semistable parabolic sheaves of rank n and fixed Euler characteristic on a disjoint union X of integral projective curves with parabolic structures over Cartier divisors on X . In the case where X is non‐singular, M is a normal projective variety. Suppose that X is the desingularisation of a reducible reduced curve Y with at most ordinary double points as singularities. We show that, for a suitable choice of parabolic structure, M ( n ) is the normalisation of the moduli space of torsion‐free sheaves of rank n and fixed Euler characteristic on Y , and it is a desingularisation if semistability coincides with stability. We find explicit descriptions of M ( n ) for small n in some cases. 1991 Mathematics Subject Classification : 14H60, 14F05.