Computing minimal Gorenstein covers
| Autor: | Roser Homs, Juan Elias, Bernard Mourrain |
|---|---|
| Přispěvatelé: | Departament de Matematiques i Informatica, Universitat de Barcelona, AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (AROMATH), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-National and Kapodistrian University of Athens (NKUA), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), European Project: 813211,H2020,POEMA(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Commutative Algebra 2010 MSC: Primary 13H10 Secondary 13H15 13P99 Computation [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] 010102 general mathematics Mathematics::Rings and Algebras Inverse Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences Effective solution Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Cover (algebra) 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 0101 mathematics Variety (universal algebra) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2019.106280⟩ Journal of Pure and Applied Algebra, Elsevier, 2019, ⟨10.1016/j.jpaa.2019.106280⟩ |
| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/j.jpaa.2019.106280⟩ |
| Popis: | We analyze and present an effective solution to the minimal Gorenstein cover problem: given a local Artin k-algebra A = k 〚 x 1 , … , x n 〛 / I , compute an Artin Gorenstein k-algebra G = k 〚 x 1 , … , x n 〛 / J such that l ( G ) − l ( A ) is minimal. We approach the problem by using Macaulay's inverse systems and a modification of the integration method for inverse systems to compute Gorenstein covers. We propose new characterizations of the minimal Gorenstein cover and present a new algorithm for the effective computation of the variety of all minimal Gorenstein covers of A for low Gorenstein colength. Experimentation illustrates the practical behavior of the method. |
| Databáze: | OpenAIRE |
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