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

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

Bastianelli, Francesco
;
2019

Abstract

In this paper we investigate the cone $Pseff_n(C_d)$ of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We study the convex-geometric properties of the cone $D_n(C_d)$ generated by the $n$-dimensional diagonal cycles. In particular we determine its extremal rays and we prove that $D_n(C_d)$ is a perfect face of $Pseff_n(C_d)$ along which $Pseff_n(C_d)$ is locally finitely generated.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/248215
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