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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1061| NUMERICAL INVARIANTS IN PRIME CHARACTERISTIC | |
| Wágner Badilla-Céspedes | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Anillos de Stanley-Reisner | |
| In prime characteristic there are important numerical invariants that allow us to detect and measure singularities. For certain cases, it is known that they are rational numbers. In the first part of this work, we show that certain F-thresholds, F-pure thresholds, and Cartier thresholds are rational numbers for Stanley-Reisner rings. In addition, we give conditions of the regularity in Stanley-Reisner rings modulo Frobenius power of ideals. The methods obtain these results rely on singularity theory in prime characteristic and the combinatorial structure of Stanley-Reisner rings. In the second part of this work, we introduce a numerical invariant called F-volume. This is motivated by the mixed test ideals associated to a sequence of ideals and their constancy regions. The F-volume extends the definition of F-threshold of an ideal to a sequence of ideals. We obtain several properties that emulate those of the F-threshold. In particular, the F-volume detects F-pure complete intersections. In addition, we relate this invariant to the Hilbert-Kunz multiplicity, and provide support for a conjecture of Núñez- Betancourt and Smirnov. Key Words | |
| 2020-06 | |
| Trabajo de grado, doctorado | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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