USHA N BHOSLE
Articles written in Proceedings – Mathematical Sciences
Volume 100 Issue 2 August 1990 pp 95-102
Singular pencils of quadrics and compactified Jacobians of curves
Let
Volume 111 Issue 3 August 2001 pp 271-291
Principal
Let
Volume 126 Issue 3 August 2016 pp 329-339 Research Article
Weak point property and sections of Picard bundles on a compactified Jacobian over a nodal curve
We show that the compactified Jacobian (and its desingularization) of an integral nodal curve $Y$ satisfies the weak point property and the Jacobian of $Y$ satisfies the diagonal property. We compute some cohomologies of Picard bundles on the compactified Jacobian and its desingularization
Volume 130 All articles Published: 11 June 2020 Article ID 0034 RESEARCH ARTICLE
Picard bundle on the moduli space of torsionfree sheaves
Let $Y$ be an integral nodal projective curve of arithmetic genus $g\geq2$ with $m$ nodes defined over an algebraically closed field. Let $n$ and $d$ be mutually coprime integers with $n\geq2$ and $d$ > $n(2g −2)$. Fix a line bundle $L$ of degree $d$ on $Y$ .We prove that the Picard bundle $E_{L}$ over the ‘fixed determinant moduli space’ $U_{L}(n, d)$ is stable with respect to the polarisation $\theta_{L}$ and its restriction to the moduli space $U'_{L}(n, d)$, of vector bundles of rank $n$ and determinant $L$, is stable with respect to any polarisation. There is an embedding of the compactified Jacobian $\bar{J}(Y)$ in the moduli space $U_{Y}(n, d)$ of rank $n$ and degree $d$. We show that the restriction of the Picard bundle of rank $ng$ (over $U_{Y}(n, n(2g − 1)))$ to $\bar{J}(Y)$ is stable with respect to any theta divisor $\theta_{\bar{J}(Y)}$.
Volume 130, 2020
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