Métodos de obtenção de geradores para as potências simbólicas - Santos, Thiago Dantas (2023)
This dissertation aims to carry out a detailed study of the symbolic powers of pure ideals over Noetherian rings, with emphasis on the determination of generators for such a class of ideals. We begin by presenting the concept, in parallel with some more elementary properties and examples. We will see some famous applications of using this powerful tool, such as Krull’s Principal Ideal Theorem, and the Zariski-Nagata Theorem. Finally, we will study some classes of ideals such as secant ideals and edge ideals, and their contributions to the determination of generators for symbolic powers, as well as the inversion factor of birational maps.