Maddaloni, Fulvio (2018) On the Lefschetz properties. [Tesi di dottorato]
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| Item Type: | Tesi di dottorato |
|---|---|
| Resource language: | English |
| Title: | On the Lefschetz properties |
| Creators: | Creators Email Maddaloni, Fulvio maddalonifulvio@gmail.com |
| Date: | 2018 |
| Number of Pages: | 93 |
| Institution: | Università degli Studi di Napoli Federico II |
| Department: | dep12 |
| Dottorato: | phd090 |
| Ciclo di dottorato: | 30 |
| Coordinatore del Corso di dottorato: | nome email De Giovanni, Francesco UNSPECIFIED |
| Tutor: | nome email Ilardi, Giovanna UNSPECIFIED |
| Date: | 2018 |
| Number of Pages: | 93 |
| Keywords: | Algebra Commutativa/Geometria Algebrica |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
| Date Deposited: | 20 Dec 2017 10:34 |
| Last Modified: | 12 Apr 2019 08:46 |
| URI: | http://www.fedoa.unina.it/id/eprint/12035 |
Collection description
The Lefschetz properties of strong type (SLP) and of weak type (WLP) are algebraic abstractions associated to the Hard Lefschetz Theorem for the cohomology ring of complex smooth projective varieties. These properties have a deep link with questions of commutative algebra, combinatorics and projective geometry. I deal with the SLP and WLP for artinian graded Gorenstein K-algebras. I study the class of the GNP- polynomials of type (m, n, k, e), introduced by R. Gondim; in particular I study the Hilbert vector of a GNP- algebra and the annihilator of the GNP-polynomial of type (m, n, k, k + 1) via the use of an associated simplicial complex. In the end I examine the geometric structure of the GNP- hypersurfaces of type (m, n, k, e).
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