Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/198423
Title: | Perazzo hypersurfaces and the Lefschetz properties |
Author: | Borrego Llebaria, Àlex |
Keywords: | Anells artinians Treballs de fi de grau Anells locals Hipersuperfícies Anells associatius Artin rings Bachelor's theses Local rings Hypersurfaces Associative rings |
Issue Date: | 24-Jan-2023 |
Abstract: | [en] The main goal of this writing is to introduce basic concepts of algebraic geometry and commutative algebra to be able to study the relationship between Perazzo hypersurfaces and the Lefschetz properties. We will introduce graded algebras and how to construct one of them from a hypersurface to further check if they satisfy any of the properties. In this paperwork, we have found an upper bound and a low enough value of the Hilbert vector for Perazzo hypersurfaces. The notable result we have obtained is that the Weak Lefschetz property is failed to obtain when the h-vector is maximal, and conversely, it is always obtained when the h-vector is on that low value. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Rosa M. Miró-Roig |
URI: | http://hdl.handle.net/2445/198423 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
tfg_borrego_llebaria_alex.pdf | Memòria | 436.86 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License