On a combinatorial description of the Gorenstein index for varieties with torus action

Philipp Iber, Eva Reinert, Milena Wrobel
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引用次数: 0

Abstract

The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope from toric geometry to wider classes of varieties. In this note we show that the Gorenstein index of Fano varieties with torus action of complexity one (and even more general of the so-called general arrangement varieties) can be read off its anticanonical complex in terms of lattice distances in full analogy to the toric Fano polytope. As an application we give concrete bounds on the defining data of almost homogeneous Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus depending on their Gorenstein index.
关于具有环作用的品种的戈伦斯坦指数的组合描述
反角复数是一种组合工具,它的发明是为了把法诺多面体的特征从环状几何扩展到更广泛的变体类别。在这篇论文中,我们证明了具有复杂度为一的环作用的法诺变种(甚至更一般的所谓一般排列变种)的戈伦斯坦指数可以从其反角复数的晶格距离中读出,这与环法诺多面体完全类似。作为应用,我们给出了皮卡数为 1 的几乎均质法诺三褶的定义数据的具体边界,这些三褶具有二维最大环的还原自变群,这取决于它们的戈伦斯坦指数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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