Doctoral Thesis
DOI
10.11606/T.55.2013.tde-09052013-150022
Document
Author
Full name
Pedro Henrique Apoliano Albuquerque Lima
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
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
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