In this paper, which is a sequel of [BKLV17], we study the convex-geometric properties of the cone of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We introduce and study the Abel–Jacobi faces, related to the contractibility properties of the Abel–Jacobi morphism and to classical Brill–Noether varieties. We investigate when Abel–Jacobi faces are non-trivial, and we prove that for $d$ sufficiently large (with respect to the genus of $C$) they form a maximal chain of perfect faces of the tautological pseudoeffective cone (which coincides with the pseudoeffective cone if $C$ is a very general curve).

中文翻译：

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曲线对称乘积上的有效循环，II：阿贝尔–雅各比面

本文是[BKLV17]的续篇，我们研究光滑曲线$ C $的对称积$ C_d $中伪有效$ n $-圈的锥的凸几何性质。我们介绍和研究Abel–Jacobi面，与Abel–Jacobi射态的可收缩性以及经典的Brill–Noether品种有关。我们调查了当Abel–Jacobi的脸不是平凡的时候，并且证明了$ d $足够大（相对于$ C $的属），它们形成了重言式伪有效锥的最大完美面链（与如果$ C $是非常普通的曲线，则为伪有效锥）。