Homomorphisms of vector bundles on curves and parabolic vector bundles on a symmetric product
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- by Indranil Biswas and Souradeep Majumder PDF
- Proc. Amer. Math. Soc. 140 (2012), 3017-3024 Request permission
Abstract:
Let $S^n(X)$ be the symmetric product of an irreducible smooth complex projective curve $X$. Given a vector bundle $E$ on $X$, there is a corresponding parabolic vector bundle ${\mathcal V}_{E*}$ on $S^n(X)$. If $E$ is nontrivial, it is known that ${\mathcal V}_{E*}$ is stable if and only if $E$ is stable. We prove that \[ H^0(S^n(X), {\mathcal H}om_\textrm {par}({\mathcal V}_{E*} , {\mathcal V}_{F*}))\!=\! H^0(X, F\otimes E^\vee )\oplus (H^0(X, F)\otimes H^0(X, E^\vee )). \] As a consequence, the map from a moduli space of vector bundles on $X$ to the corresponding moduli space of parabolic vector bundles on $S^n(X)$ is injective.References
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Additional Information
- Indranil Biswas
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
- MR Author ID: 340073
- Email: indranil@math.tifr.res.in
- Souradeep Majumder
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
- Email: souradip@math.tifr.res.in
- Received by editor(s): March 29, 2011
- Published electronically: January 24, 2012
- Communicated by: Lev Borisov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3017-3024
- MSC (2010): Primary 14F05, 14H60
- DOI: https://doi.org/10.1090/S0002-9939-2012-11227-4
- MathSciNet review: 2917074