Deformations of the Picard Bundle

Details Deformations of the Picard Bundle Deformations of the Picard Bundle

2001-04-17

arxiv.org/abs/math/0104170v2

Mathematics

Algebraic Geometry

14 pages, AMSLatex, introduction rewritten, minor additions, new references

Scientific paper

Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider the moduli space M of stable bundles of fixed determinant with rank n and degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we consider the direct image of this bundle on M. With the given restriction on d, this is a bundle W called the Picard bundle. Our main object in this paper is to compute the infinitesimal deformations of W. We show also that W possesses a moduli space and that the connected component of this moduli space containing W is isomorphic as a polarised variety to the Jacobian of X.

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