Usha N Bhosle
Articles written in Proceedings – Mathematical Sciences
Volume 102 Issue 1 April 1992 pp 13-22
Generalized parabolic sheaves on an integral projective curve
We extend the notion of a parabolic vector bundle on a smooth curve to define generalized parabolic sheaves (GPS) on any integral projective curve X. We construct the moduli spaces
Volume 106 Issue 4 November 1996 pp 403-420
Generalized parabolic bundles and applications— II
We prove the existence of the moduli space
Volume 114 Issue 2 May 2004 pp 107-122
Picard groups of the moduli spaces of semistable sheaves I
We compute the Picard group of the moduli space
Volume 115 Issue 4 November 2005 pp 445-451
Vector bundles with a fixed determinant on an irreducible nodal curve
Let
Volume 118 Issue 1 February 2008 pp 81-98
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over $\mathbb{C}$. Let 𝑋 be a nodal curve of arithmetic genus one defined over $\mathbb{R}$, with exactly one node, such that 𝑋 does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over 𝑋 of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over 𝑋 of rank one.
Volume 123 Issue 3 August 2013 pp 331-344
We compute the cohomology of the Picard bundle on the desingularization $\overline{J}^d (Y)$ of the compactified Jacobian of an irreducible nodal curve 𝑌. We use it to compute the cohomology classes of the Brill–Noether loci in $\overline{J}^d(Y)$.
We show that the moduli space 𝑀 of morphisms of a fixed degree from 𝑌 to a projective space has a smooth compactification. As another application of the cohomology of the Picard bundle, we compute a top intersection number for the moduli space 𝑀 confirming the Vafa–Intriligator formulae in the nodal case.
Volume 131, 2021
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