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摘要翻译：
Mats Boij和Jonas Soederberg(Math.AC/0611081)推测多项式环上Cohen-Macaulay模的Betti表可以以某种方式分解为纯分辨率模的Betti表的正线性组合。我们在任何领域证明了他们猜想的一个加强形式。应用包括Huneke和Srinivasan的多重猜想的证明以及与Young格自然相关的扇形凸性的证明。我们还用超自然丛的上同调表刻划了射影空间上所有向量丛的上同调表的有理锥。在某种意义上，这个刻划与我们对Betti表的刻划是对偶的。
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英文标题：
《Betti Numbers of Graded Modules and Cohomology of Vector Bundles》
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作者：
David Eisenbud and Frank-Olaf Schreyer
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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：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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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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英文摘要：
Mats Boij and Jonas Soederberg (math.AC/0611081) have conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring can be decomposed in a certain way as a positive linear combination of Betti tables of modules with pure resolutions. We prove, over any field, a strengthened form of their conjecture. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fan naturally associated to the Young lattice. We also characterize the rational cone of all cohomology tables of vector bundles on projective spaces in terms of the cohomology tables of "supernatural" bundles. This characterization is dual, in a certain sense, to our characterization of Betti tables.
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PDF链接：
https://arxiv.org/pdf/0712.1843
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