Maddaloni, Fulvio (2018) On the Lefschetz properties. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Lingua: English
Title: On the Lefschetz properties
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:
De Giovanni, FrancescoUNSPECIFIED
Ilardi, GiovannaUNSPECIFIED
Date: 2018
Number of Pages: 93
Uncontrolled 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


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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