论文标题
有限的考克斯戒指
Finite generation of Cox rings
论文作者
论文摘要
在此说明中，我们讨论了一类名为Cox环的分级代数，这些代数与代数品种自然相关，从而概括了投射空间的均匀坐标环。每当有限地生成Cox环时，该品种都会接受Quasitorus的商演示，类似于投射空间的商结构。我们从几何角度讨论了Cox环有限生成的问题，并提供了有限和非最初生成的情况的示例。
In this expository note we discuss a class of graded algebras named Cox rings, which are naturally associated to algebraic varieties generalizing the homogeneous coordinate rings of projective spaces. Whenever the Cox ring is finitely generated, the variety admits a quotient presentation by a quasitorus, which resembles the quotient construction of the projective space. We discuss the problem of the finite generation of Cox rings from a geometric perspective and provide examples of both the finitely and non-finitely generated cases.
