Arithmetic degree and associated graded modules

Vinai, Natale Paolo

doi:10.1007/s00229-004-0492-7

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Proof Consider the Exact Sequences Induced By Multiplication By1

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2014

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“…Some (consider the case of the I-adic filtration) occur simply by considering the passage R → R[It, t −1 ] followed by the hyperplane section t −1 . Other detailed information is found by a direct analysis (see [204]).…”

Section: Proof Consider the Exact Sequences Induced By Multiplication Bymentioning

confidence: 99%

Complexity Degrees of Algebraic Structures

Vasconcelos

2014

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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: Proof Consider the Exact Sequences Induced By Multiplication Bymentioning

confidence: 99%

Complexity Degrees of Algebraic Structures

Vasconcelos

2014

Preprint

View full text Add to dashboard Cite

show abstract

Arithmetic degree and associated graded modules

Cited by 1 publication

References 14 publications

Complexity Degrees of Algebraic Structures

Complexity Degrees of Algebraic Structures

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