Geodesic
Automorphisms of a Symmetric Product of a Curve (with an Appendix by Najmuddin Fakhruddin)
Documenta mathematica, Tome 22 (2017), pp. 1181-1192.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14H40, 14J50
Keywords: symmetric product, automorphism, Torelli theorem 
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Biswas, Indranil; Gómez, Tomás L. Automorphisms of a Symmetric Product of a Curve (with an Appendix by Najmuddin Fakhruddin). Documenta mathematica, Tome 22 (2017), pp. 1181-1192. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a18/