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arXiv · 2210.11829

Effective cone of the blow up of the symmetric product of a curve

Antonio Laface·Luca Ugaglia
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Abstract

Let $C$ be a smooth curve of genus $g \geq 1$ and let $C^{(2)}$ be its second symmetric product. In this note we prove that if $C$ is very general, then the blow-up of $C^{(2)}$ at a very general point has non-polyhedral pseudo-effective cone. The strategy is to consider first the case of hyperelliptic curves and then to show that having polyhedral pseudo-effective cone is a closed property for families of surfaces.

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Antonio Laface, Luca Ugaglia. 2022-10-21. Effective cone of the blow up of the symmetric product of a curve. https://arxiv.org/abs/2210.11829

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