TY - JOUR
T1 - Divisor Varieties of Symmetric Products
AU - Sheridan, John
N1 - Publisher Copyright:
© The Author(s) 2021.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnaa313
DO - 10.1093/imrn/rnaa313
M3 - Article
AN - SCOPUS:85134364590
SN - 1073-7928
VL - 2022
SP - 9830
EP - 9863
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 13
ER -