Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons
Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons
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有理凸多边形艾哈特环放大负曲线方程组
DOI：
10.1016/j.jalgebra.2021.10.016
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kazuhiko Kurano
中科院分区：
文献类型：
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作者：
Kazuhiko Kurano
三维加权多项式环的空间单项素理想的符号Rees环的有限生成是一个非常有趣的问题。负曲线在这些环的有限生成中起着重要的作用。我们感兴趣的是负曲线的结构。我们将证明负曲线在许多情况下是有理的。我们还看到复曲面簇在点（1，1，.，1）处爆破的考克斯环与多项式环的理想的扩展符号Rees环重合。例如，罗伯茨的第二个反例考西克的问题（和希尔伯特的第14个问题）符合考克斯环的一些正常的投射品种（注2.7）。
Finite generation of the symbolic Rees ring of a space monomial prime ideal of a 3-dimensional weighted polynomial ring is a very interesting problem. Negative curves play important roles in finite generation of these rings. We are interested in the structure of the negative curve. We shall prove that negative curves are rational in many cases. We also see that the Cox ring of the blow-up of a toric variety at the point (1, 1,…, 1) coincides with the extended symbolic Rees ring of an ideal of a polynomial ring. For example, Roberts' second counterexample to Cowsik's question (and Hilbert's 14th problem) coincides with the Cox ring of some normal projective variety (Remark 2.7).