Seshadri constants on symmetric products of curves

• Autores: J. Ross
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 1, 2007, págs. 63-75
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n1.a5
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• Resumen

  • Let $X_g=C^{(2)}_g$ be the second symmetric product of a very general curve of genus $g$. We reduce the problem of describing the ample cone on $X_g$ to a problem involving the Seshadri constant of a point on $X_{g-1}$. Using this we recover a result of Ciliberto-Kouvidakis that reduces finding the ample cone of $X_g$ to the Nagata conjecture when $g\ge 9$. We also give new bounds on the the ample cone of $X_g$ when $g=5$.