• Maps into Projective Spaces

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/123/03/0331-0344

    • 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

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.