Sobre a fibra especial e o teorema de Risler-Teissier para filtrações

Lima, Pedro Henrique Apoliano Albuquerque

doi:10.11606/T.55.2013.tde-09052013-150022

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2013.tde-09052013-150022

Document

Doctoral Thesis

Author

Lima, Pedro Henrique Apoliano Albuquerque (Catálogo USP)

Full name

Pedro Henrique Apoliano Albuquerque Lima

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2013-02-26

Published

São Carlos, 2013

Supervisor

Pérez, Victor Hugo Jorge (Catálogo USP)

Committee

Pérez, Victor Hugo Jorge (President)
Brumatti, Paulo Roberto
Hefez, Abramo
Levcovitz, Daniel
Orihuela, Fernando Eduardo Torres

Title in Portuguese

Sobre a fibra especial e o teorema de Risler-Teissier para filtrações

Keywords in Portuguese

Fibra especial
O Teorema de Risler-Teissier para filtações
Propriedae da fibra especial ser Gorenstein
Regularidade de Castelnuovo-Mumford

Abstract in Portuguese

Seja (R;m) um anel Noetheriano local e R 'CONTÉM' 'iota IND. 1' 'CONTÉM' 'iota IND. 2' 'CONTÉM ... uma filtração de ideais de R. Podemos então construir a álgebra graduada F('\Im) := 'SOMA DIRETA IND. n > OU = 0 POT. 'iota IND. n / 'm 'iota IND. n', chamada de fibra especial. Esta tese objetiva a pesquisa deste anel. Investigamos sobre a sua propriedade de ser Gorenstein e a sua regularidade de Castelnuovo-Mumford. Outro objetivo, é generalizarmos o teorema de Risler-Teissier (sobre multiplicidades mistas) para o caso de filtrações de Hilbert

Title in English

On fiber cone and Risler-Teissier theorem to fibration

Keywords in English

Castelnuovo-Mumford regularity
Fiber cone
Gorenstein property
Risler-Teissier theorem to fibration

Abstract in English

Let (R;m) be a Noetherian local ring and R 'CONTAINS' 'iota IND. 1' 'CONTAINS' 'iota IND. 2' 'CONTAINS' ... a filtration of ideals in R. We may then construct the graded algebra F(\Im) := 'DIRECT SUM' IND. n > OR = '0 POT. 'iota' IND. n / 'm 'iota IND. n' , which is called fiber cone. This thesis has the goal to research about this graded ring. We investigate its Gorenstein property and its Castelnuovo-Mumford regularity. Another aim is to generalize the Risler-Teissiers theorem (about mixed multiplicities) for the case of Hilbert filtration

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Publishing Date

2013-05-10

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