摘要翻译：
在他关于重数的对数凹性的工作中，Okounkov顺便指出，人们可以把凸体与射影簇上的线性级数联系起来，然后用凸几何来研究这样的线性系统。尽管Okounkov基本上是在大量线束的经典设置中工作的，但事实证明，构造过程是针对任意的大除数进行的。此外，这一观点使关于线性级数渐近不变量的许多基本事实变得透明，并为许多推广打开了大门。本文的目的是对该理论进行系统的发展，并给出一些应用和实例。
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英文标题：
《Convex Bodies Associated to Linear Series》
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作者：
Robert Lazarsfeld, Mircea Mustata
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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：
  In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study such linear systems. Although Okounkov was essentially working in the classical setting of ample line bundles, it turns out that the construction goes through for an arbitrary big divisor. Moreover, this viewpoint renders transparent many basic facts about asymptotic invariants of linear series, and opens the door to a number of extensions. The purpose of this paper is to initiate a systematic development of the theory, and to give a number of applications and examples.
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PDF链接：
https://arxiv.org/pdf/0805.4559