Sessa, Carmine (2022) On the BBDG's decomposition theorem. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | On the BBDG's decomposition theorem |
| Autori: | Autore Email Sessa, Carmine carmine.sessa2@unina.it |
| Data: | 13 Dicembre 2022 |
| Numero di pagine: | 98 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 35 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda dottorato.dma@unina.it |
| Tutor: | nome email Marino, Giuseppe [non definito] |
| Data: | 13 Dicembre 2022 |
| Numero di pagine: | 98 |
| Parole chiave: | Decomposition theorem, Schubert varieties, Kazhdan-Lusztig polynomials, Bivariant theory, Homology manifolds, Nilpotent cone |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
| Depositato il: | 03 Gen 2023 10:21 |
| Ultima modifica: | 09 Apr 2025 14:16 |
| URI: | http://www.fedoa.unina.it/id/eprint/14654 |
Abstract
The thesis is a collection of the results achieved during the PhD. The (Beilinson, Bernstein, Deligne and Gabber) BBDG’s decomposition theorem plays a central role and, therefore, the preliminary chapter is devoted to definitions and properties necessary to enlighten such result. As a first application of such theorem, Schubert varieties in a Grassmannian are examined so as to show classes of examples in which the decomposition provided by the theorem is not as esoteric as in general. As a by-product, the obtained information concerning the direct summands provide an algorithm for the computation of some of the so-called Kazhdan-Lusztig polynomials. The second application of the BBDG’s theorem, nay, of an analogous decomposition available for a broader family of rings, is the investigation of a connection between the existence of bivariant classes of degree one and the property of certain topological spaces of being homology manifolds. In particular, the achieved results provide a simple new proof of the fact that Nilpotent cones are homology manifolds.
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