• Maps into Projective Spaces

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    • Keywords


      Nodal curves; torsionfree sheaves; Picard bundle.

    • Abstract


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

      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.

    • Author Affiliations


      Usha N Bhosle1

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

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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