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Multiplicity, mixed multiplicities, Hilbert coefficient for modules and equisingularity

Grant number: 12/20304-1
Support type:Scholarships abroad - Research
Effective date (Start): October 01, 2013
Effective date (End): September 30, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Victor Hugo Jorge Pérez
Grantee:Victor Hugo Jorge Pérez
Host: Bernd Ulrich
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Local de pesquisa : Purdue University, United States  

Abstract

In recent years, using different sequences, expressed he mixed multiplicity in terms of the Hilbert-Samuel multiplicity, for example, in the case of m-primary ideals, Risler-Teissier in 1973 showed that each mixed multiplicity is the Hilbert-Samuel multiplicity of an ideal generated by a sequence superficial, then this was generalized to m-primary ideals using notions of joint reduction to a family of ideals, this result is called the fundamental theorem of Rees for multiplicities. This theorem is very important in commutative algebra and geometry. Therefore we intend obter the reciprocal of this theorem and make a study of multiplicities, mixed multiplicities of arbitrary ideals and modules. (AU)

Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CHU, L. Z.; JORGE PEREZ, V. H.; LIMA, P. H. Ideal transforms and local cohomology defined by a pair of ideals. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 17, n. 10 OCT 2018. Web of Science Citations: 0.
CHU, LIZHONG; JORGE PEREZ, V. H. The Stanley regularity of complete intersections and ideals of mixed products. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 16, n. 7 JUL 2017. Web of Science Citations: 0.
FREITAS, T. H.; JORGE PEREZ, V. H. Artinianness and finiteness of formal local cohomology modules with respect to a pair of ideals. BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, v. 58, n. 2, p. 319-340, JUN 2017. Web of Science Citations: 1.
CALLEJAS-BEDREGAL, R.; JORGE PEREZ, V. H. ON LECH'S LIMIT FORMULA FOR MODULES. Colloquium Mathematicum, v. 148, n. 1, p. 27-37, 2017. Web of Science Citations: 0.
LIMA, P. H.; JORGE PEREZ, V. H. GRADED VERSION OF LOCAL COHOMOLOGY WITH RESPECT TO A PAIR OF IDEALS. JOURNAL OF COMMUTATIVE ALGEBRA, v. 9, n. 4, p. 545-561, WIN 2017. Web of Science Citations: 1.
LIMA, P. H.; JORGE PEREZ, V. H. EQUIMULTIPLE COEFFICIENT IDEALS. MATHEMATICA SCANDINAVICA, v. 121, n. 1, p. 5-18, 2017. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.