Automorphisms of a symmetric product of a curve (with an appendix by Najmuddin Fakhruddin)
Summary: Let \(X\) be an irreducible smooth projective curve of genus \(g>2\) defined over an algebraically closed field of characteristic different from two. We prove that the natural homomorphism from the automorphisms of \(X\) to the automorphisms of the symmetric product \(\mathrm{Sym}^d(X)\) is an isomorphism if \(d>2g-2\). In an appendix, Fakhruddin proves that the isomorphism class of the symmetric product of a curve determines the isomorphism class of the curve.
scientific article; zbMATH DE number 6810408
scientific article