On Cox rings of K3 surfaces
On Cox rings of K3 surfaces
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在 K3 表面的 Cox 环上
作者：
M. Artebani;J. Hausen;A. Laface
摘要研究了K3曲面上的Cox环。第一个结果是K3曲面有一个有限生成的Cox环当且仅当它的有效锥是有理多面体。此外，我们还研究了Picard数为2的K3曲面的生成元次和Cox环之间的关系，并显式地计算了具有Picard数为2到5的非辛对合或作为del Pezzo曲面的双覆盖的一般K3曲面的Cox环。
Abstract We study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.