Divisor Varieties of Symmetric Products

Research output: Contribution to journalArticlepeer-review


The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and dimension) are smooth, irreducible projective varieties of known dimension. For higher dimensional varieties, the story is less well understood. Our purpose in this paper is to study in detail one class of higher dimensional examples where one can hope for a quite detailed picture, namely (the spaces parametrizing) divisors on the symmetric product of a curve.

Original languageEnglish (US)
Pages (from-to)9830-9863
Number of pages34
JournalInternational Mathematics Research Notices
Issue number13
StatePublished - Jul 1 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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