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Seshadri constants on symmetric products of curves

J. Ross
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Abstract

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.

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J. Ross. 2006-09-05. Seshadri constants on symmetric products of curves. https://arxiv.org/abs/math/0608224

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