局部上同调模的lex-plus-power不等式
The lex-plus-power inequality for local cohomology modules
摘要：
在Hilbert函数偏序集嵌入的框架下，证明了域上标准分次代数的齐次极大理想所支持的局部上同调模的Hilbert函数之间的一个不等式.作为一个主要应用，我们证明了Evans的Lex-Plus-Power猜想在贝蒂数上的一个类似的局部上同调.这一结果包含了经典的Lex-Plus-Power猜想的某些情形，即极值贝蒂数之间的一个不等式.特别地，对于目前已知的Eisenbud-Green-Harris猜想的理想类，分次理想的投射维数和Castelnuovo-Mumford正则性不会通过传递到相应的Lex-Plus-Power理想而减少。
英文摘要：
We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main application, we prove an analogue for local cohomology of Evans' Lex-Plus-Power Conjecture for Betti numbers. This results implies some cases of the classical Lex-Plus-Power Conjecture, namely an inequality between extremal Betti numbers. In particular, for the classes of ideals for which the Eisenbud-Green-Harris Conjecture is currently known, the projective dimension and the Castelnuovo-Mumford regularity of a graded ideal do not decrease by passing to the corresponding Lex-Plus-Power ideal.
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