Torelli's theorem for high degree symmetric products of curves

Abstract

We show that two smooth projective curves C_1 and C_2 of genus g which have isomorphic symmetric products are isomorphic unless g=2. This extends a theorem of Martens.

D. Huybrechts has pointed out an error in the proof when g = 2. Also, we were recently informed that the result in the case g > 2 was proved earlier by Ciliberto and Miranda in "On the symmetric products of a curve", Arch. Math. (61), 285-290, 1993

Cited by in corpus (3)

• On the Kaehler metrics over ${mathrm{Sym}^{d}(X)$
• Automorphisms of a symmetric product of a curve
• On Brill-Noether loci over Quot schemes and a Torelli theorem