Banca de DEFESA: GEISA GAMA OLIVEIRA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE: GEISA GAMA OLIVEIRA
DATA : 27/11/2025
HORA: 10:00
LOCAL: https://meet.google.com/etr-ymqs-nvg
TÍTULO:

Topics on perfect ideals of codimension two

 

PALAVRAS-CHAVES:

Monomial ideals, plane reduced points, special fiber, perfect ideal of codimension two, Rees algebra, Cohen–Macaulay.

 

PÁGINAS: 67
RESUMO:

In this work, we are interested in perfect ideals $I$ of codimension two in a polynomial ring $R$ over a field of characteristic zero. The overall interest is on the homological nature of the main algebras related to the HilbertBurch syzygy matrix associated to $I$, in particular on the Cohen-Macaulay property of the Rees algebra and the special fiber of $I$. We develop this study in three contexts: monomial ideals, ideals defined by the $2$minors of homogeneous $3\times2$ matrices, and the defining ideal of a finite set of reduced points in projective $2$-space. In addition, we investigate geometric aspects related to these ideals, focusing on how their algebraic properties are reflected in the associated rational maps.

MEMBROS DA BANCA:
Externa à Instituição - ALINE VILELA ANDRADE - UFMG
Externo à Instituição - RICARDO BURITY CROCCIA MACEDO - UFPB
Presidente - 287157 - ARON SIMIS
Externa à Instituição - BARBARA COSTA DA SILVA - UFRPE
Interno - 3409415 - RAFAEL FERREIRA HOLANDA