Normal Hilbert Polynomials : A survey

Mandal, Mousumi; Masuti, Shreedevi K.; Verma, J. K.

doi:10.48550/arxiv.1205.3342

Cited by 2 publications

(1 citation statement)

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“…Remark 2.3.5. For normal ideals the information about the Hilbert function is very detailed-see, for instance a modern survey in [123]. It remains a goal to have for general normalizations that level of specificity.…”

Section: Indices Of Normalizationmentioning

confidence: 99%

Complexity Degrees of Algebraic Structures

Vasconcelos

2014

Preprint

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We aim at studying collections C(R) of algebraic structures defined over a commutative ring R and investigating the complexity of significant constructions carried out on these objects. Noteworthy are the category of finitely generated modules (over local rings, or graded, particularly vector bundles), finitely generated algebras or objects suitable of more fundamental decompositions and construction of various closure operations-such as the determination of global sections and the (theoretical or machine) computation of integral closures of algebras. Typically, the operations express smoothing processes that enhance the structure of the algebras, enable them to support new constructions (including analytic ones), divisors acquire a group structure, and the cohomology tends to slim down. The assignment of measures of size, via a multiplicity theory, to the algebras and to the construction itself is a novel aspect to the subject. One of its specific goals is to develop a comprehensive theory of normalization in commutative algebra and a broad set of multiplicity functions to be used as complexity benchmarks.

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Section: Indices Of Normalizationmentioning

confidence: 99%