• Picard bundle on the moduli space of torsionfree sheaves

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    • Keywords


      Nodal curve; moduli spaces; Picard bundles; stability.

    • Abstract


      Let $Y$ be an integral nodal projective curve of arithmetic genus $g\geq2$ with $m$ nodes defined over an algebraically closed field. Let $n$ and $d$ be mutually coprime integers with $n\geq2$ and $d$ > $n(2g −2)$. Fix a line bundle $L$ of degree $d$ on $Y$ .We prove that the Picard bundle $E_{L}$ over the ‘fixed determinant moduli space’ $U_{L}(n, d)$ is stable with respect to the polarisation $\theta_{L}$ and its restriction to the moduli space $U'_{L}(n, d)$, of vector bundles of rank $n$ and determinant $L$, is stable with respect to any polarisation. There is an embedding of the compactified Jacobian $\bar{J}(Y)$ in the moduli space $U_{Y}(n, d)$ of rank $n$ and degree $d$. We show that the restriction of the Picard bundle of rank $ng$ (over $U_{Y}(n, n(2g − 1)))$ to $\bar{J}(Y)$ is stable with respect to any theta divisor $\theta_{\bar{J}(Y)}$.

    • Author Affiliations



      1. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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