Generalized parabolic bundles and applications. II. (English) Zbl 0879.14012
The author further develops her theory of generalized parabolic bundles (vector bundles with flags of vector spaces over effective divisors) on smooth curves, initiated in part I of this paper [U. N. Bhosle, Ark. Mat. 30, No. 2, 187-215 (1992; Zbl 0773.14006)]. In that paper, she considered the special case of flags of length 2. In the paper under review, the author considers flags of sufficiently general type and proves the existence of the moduli space \(M(n,d)\) of semistable generalized parabolic bundles of rank \(n\) and degree \(d\). She studies some interesting cases of such moduli spaces and finds explicit geometric descriptions for them in low ranks and genera. The author also defines the subvariety \(M_L (n,d)\) corresponding to the semistable generalized parabolic bundles with fixed determinant \(L\), where \(L\) is a generalized parabolic bundle of rank 1. She applies her results to the study of moduli spaces of torsion free sheaves on a reduced irreducible curve with nodes and ordinary cusps as singularities.
Reviewer: I.Coandă (Bucureşti)
MSC:
| 14H60 | Vector bundles on curves and their moduli |
| 14H20 | Singularities of curves, local rings |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
Keywords:
nodal curves; torsion free sheaves; generalized parabolic bundles; flags of vector spaces; moduli spacesCitations:
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