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摘要翻译：
利用有理函数域上构型诱导的sagbi基，将Cox-Nagata环退化为toric代数。对于del Pezzo曲面，这种退化意味着Batyrev-Popov猜想，即这些环是由二次曲面的理想表示的。对于射影n-空间在n+3点上的爆破，Cox-Nagata环的sagbi基在Verlinde公式和系统发生代数几何之间建立了联系，我们用它来回答D'Cruz-Iarobbino和Buczynska-Wisniewski提出的问题。受Holtz和Ron的zonotopal代数的启发，我们的研究强调显式计算，并提供了一种新的方法来求解胖点的Hilbert函数。
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英文标题：
《Sagbi Bases of Cox-Nagata Rings》
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作者：
Bernd Sturmfels and Zhiqiang Xu
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev-Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n+3 points, sagbi bases of Cox-Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D'Cruz-Iarobbino and Buczynska-Wisniewski. Inspired by the zonotopal algebras of Holtz and Ron, our study emphasizes explicit computations, and offers a new approach to Hilbert functions of fat points.
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PDF链接：
https://arxiv.org/pdf/0803.0892
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