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摘要翻译：
设x\子集pp^n是域上的射影方案，设phi:x-->Y是有限态射。我们的主要结果是根据全局数据导出了\phi纤维的Castelnuovo-Mumford正则性的最大值公式，并将其视为\pp^n的子格式。从代数的观点出发，我们的公式与Cutkosky-Herzog-Trung和Kodiyalam的定理有关。该定理表明，对于标准分次代数S中的任意齐次理想I，对于某些非负整数d，ε，以及所有大的T，I^t的正则性可以写成dt+ε.在I包含S+的幂并由一次形式生成的特殊情况下，我们的公式给出了\ε的解释：它比与I有关的态射的纤维的最大正则性小一个。这些公式对由泛型形式生成的理想有很强的结果。
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英文标题：
《Powers of Ideals and Fibers of Morphisms》
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作者：
David Eisenbud and Joe Harris
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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：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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英文摘要：
Let X\subset PP^n be a projective scheme over a field, and let phi:X --> Y be a finite morphism. Our main result is a formula in terms of global data for the maximum of the Castelnuovo-Mumford regularity of the fibers of \phi, considered as subschemes of \PP^n. From an algebraic point of view, our formula is related to the theorem of Cutkosky-Herzog-Trung and Kodiyalam showing that for any homogeneous ideal I in a standard graded algebra S, the regularity of I^t can be written as dt+\epsilon for some non-negative integers d, \epsilon, and all large t. In the special case where I contains a power of S_+ and is generated by forms of a single degree, our formula gives an interpretation of \epsilon: it is one less than the maximum regularity of a fiber of the morphism associated to I. These formulas have strong consequences for ideals generated by generic forms.
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PDF链接：
https://arxiv.org/pdf/0807.4243
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