Effective cycles on the symmetric product of a curve, I: the diagonal cone. (with an appendix by Ben Moonen)

Francesco Bastianelli; Alexis Kouvidakis; Angelo Felice Lopez; Filippo Viviani

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arXiv · 1711.07722

Effective cycles on the symmetric product of a curve, I: the diagonal cone. (with an appendix by Ben Moonen)

Francesco Bastianelli·Alexis Kouvidakis·Angelo Felice Lopez·Filippo Viviani

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Abstract

In this paper and in its sequel [BKLV], we investigate the cone ${\rm Pseff}_n(C_d)$ of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. In the present paper, we study the convex-geometric properties of the cone generated by the $n$-dimensional diagonal cycles, which we call the $n$-dimensional diagonal cone. We prove that the $n$-dimensional diagonal cone is a perfect face of ${\rm Pseff}_n(C_d)$ along which ${\rm Pseff}_n(C_d)$ is locally finitely generated.

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Francesco Bastianelli, Alexis Kouvidakis, Angelo Felice Lopez, Filippo Viviani. 2017-11-21. Effective cycles on the symmetric product of a curve, I: the diagonal cone. (with an appendix by Ben Moonen). https://arxiv.org/abs/1711.07722

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