Journal of the Ramanujan Mathematical Society

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Vector Bundles on Symmetric Product of a Curve


Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India
2 Kerala School of Mathematics, Kunnamangalam (PO), Kozhikode-673571, Kerala, India
     

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Let X be an irreducible smooth projective curve defined over ℂ. Fix any integer n≥2. There is a tautological hypersurface Δ∈X×Sn(X), where Sn(X) is the symmetric product. Given any vector bundle E over X, let F(E) be the vector bundle on Sn(X) obtained by taking the direct image of the pullback of E to Δ. Let E and F be semi-stable vector bundles over X such that μ(E),μ(F)>n-1. If F(E) is isomorphic to F(F), then we prove that E is isomorphic to F.
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  • Vector Bundles on Symmetric Product of a Curve

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Authors

Indranil Biswas
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India
A. J. Parameswaran
Kerala School of Mathematics, Kunnamangalam (PO), Kozhikode-673571, Kerala, India

Abstract


Let X be an irreducible smooth projective curve defined over ℂ. Fix any integer n≥2. There is a tautological hypersurface Δ∈X×Sn(X), where Sn(X) is the symmetric product. Given any vector bundle E over X, let F(E) be the vector bundle on Sn(X) obtained by taking the direct image of the pullback of E to Δ. Let E and F be semi-stable vector bundles over X such that μ(E),μ(F)>n-1. If F(E) is isomorphic to F(F), then we prove that E is isomorphic to F.