A remark on a conjecture of Paranjape and Ramanan

  • Friedrich Eusen

    Düsseldorf, Germany
  • Frank-Olaf Schreyer

    Universität des Saarlandes, Saarbrücken, Germany
A remark on a conjecture of Paranjape and Ramanan cover
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Abstract

In this note, we show that the spaces of global sections of exterior powers of a globally generated line bundle on a curve are not necessarily spanned by locally decomposable sections. The examples are based on the study of generic syzygy varieties. An application of these varieties is a short proof of Mukai's theorem that every smooth curve of genus 7 and Clifford index 3 arises as the intersection of the spinor variety with a transversal .