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Maps into projective spaces

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Abstract

We compute the cohomology of the Picard bundle on the desingularization \(\tilde{J}^d(Y)\) of the compactified Jacobian of an irreducible nodal curve Y. We use it to compute the cohomology classes of the Brill–Noether loci in \(\tilde{J}^d(Y)\).

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.

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Acknowledgements

This work was initiated during the author’s visit to the Isaac Newton Institute, Cambridge, UK as a visiting fellow to participate in the programme Moduli Spaces (MOS) during June 2011. She would like to thank the Institute for hospitality and excellent working environment.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    USHA N BHOSLE

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  1. USHA N BHOSLE
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Correspondence to USHA N BHOSLE.

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BHOSLE, U.N. Maps into projective spaces. Proc Math Sci 123, 331–344 (2013). https://doi.org/10.1007/s12044-013-0135-6

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  • DOI: https://doi.org/10.1007/s12044-013-0135-6

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