Effective cycles on the symmetric product of a curve, I: the diagonal cone

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

doi:10.1090/tran/7867

Effective cycles on the symmetric product of a curve, I: the diagonal cone
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by Francesco Bastianelli, Alexis Kouvidakis, Angelo Felice Lopez and Filippo Viviani; with an appendix by Ben Moonen PDF

Trans. Amer. Math. Soc. 372 (2019), 8709-8758 Request permission

Abstract:

In this paper we investigate the cone $\operatorname {Pseff}_n(C_d)$ of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We study the convex-geometric properties of the cone $\mathcal {D}_n(C_d)$ generated by the $n$-dimensional diagonal cycles. In particular we determine its extremal rays and we prove that $\mathcal {D}_n(C_d)$ is a perfect face of $\operatorname {Pseff}_n(C_d)$ along which $\operatorname {Pseff}_n(C_d)$ is locally finitely generated.

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