The purpose of this short note is to study dominant rational maps frompunctual Hilbert schemes of length $k>1$ of projective K3 surfaces $S$containing infinitely many rational curves. Precisely, we prove that theirimage is necessarily rationally connected if this rational map is notgenerically finite. As an application, we simplify the proof of C. Voisin's ofthe fact that symplectic involutions of any projective K3 surface $S$ acttrivially on $\mathrm{CH}_0(S)$.
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机译：本简短笔记的目的是研究长度为k且射影K3曲面$ S $包含无限多个有理曲线的点Hilbert方案的主要有理图。确切地说，我们证明，如果此有理图不是一般地有限的，则它们的图像必定是有合理联系的。作为应用程序，我们简化了C. Voisin的证明，即任何射影K3的辛内卷在$ \ mathrm {CH} _0（S）$上实际作用于$ S $。
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