Hilbert functions and Jordan type of Perazzo Artinian algebras

Autor:	Abdallah, Nancy, Altafi, Nasrin, De Poi, Pietro, Fiorindo, Luca, Iarrobino, Anthony, Marques, Pedro Macias, Mezzetti, Emilia, Miró-Roig, Rosa M., Nicklasson, Lisa
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry 13E10 (primary) 13D40 14M05 13H10
Druh dokumentu:	Working Paper
Popis:	We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smallest possible Hilbert function, we give a description of the possible Jordan types for multiplication by any linear form. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.16768 Zobrazit plný text záznamu View this record from Arxiv