Geodesic
Automorphisms of a Symmetric Product of a Curve (with an Appendix by Najmuddin Fakhruddin)
Documenta mathematica, Tome 22 (2017), pp. 1181-1192
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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 Symd(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.
DOI : 10.4171/dm/591
Classification : 14H40, 14J50
Mots-clés : symmetric product, Torelli theorem, automorphism 
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     author = {Indranil Biswas and Tom\'as L. G\'omez},
     title = {Automorphisms of a {Symmetric} {Product} of a {Curve} (with an {Appendix} by {Najmuddin} {Fakhruddin)}},
     journal = {Documenta mathematica},
     pages = {1181--1192},
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     volume = {22},
     doi = {10.4171/dm/591},
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Indranil Biswas; Tomás L. Gómez. Automorphisms of a Symmetric Product of a Curve (with an Appendix by Najmuddin Fakhruddin). Documenta mathematica, Tome 22 (2017), pp. 1181-1192. doi: 10.4171/dm/591

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