2,777 research outputs found
Prefazione a Carlo Perazzo, In-comune. Nessi per un’antropologia ecologica.
No full textPresentazione del volume di Carlo Perazzo, all'incrocio fra antropologia, ecologia e critica sociale
Hilbert Functions and Jordan Type of Perazzo Artinian Algebras
No full textWe 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.</p
Hilbert Functions and Jordan Type of Perazzo Artinian Algebras
No full textWe 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. </p
Perazzo n-folds and the weak Lefschetz property
No full textIn this paper, we determine the maximum h_max and the minimum h_min of the Hilbert vectors of Perazzo algebras A_F, where F is a Perazzo polynomial of degree d in n+m+1 variables. These algebras always fail the Strong Lefschetz Property. We determine the integers n, m, d such that h_max (resp. h_min) is unimodal, and we prove that A_F always fails the Weak Lefschetz Property if its Hilbert vector is maximum, while it satisfies the Weak Lefschetz Property if it is minimum, unimodal, and satisfies an additional mild condition. We determine the minimal free resolution of Perazzo algebras associated to Perazzo threefolds in P^4 with minimum Hilbert vectors. Finally we pose some open problems in this context
Hilbert functions and Jordan type of Perazzo Artinian algebras
No full textWe 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
Perazzo 3-folds and the weak Lefschetz property
No full textWe deal with Perazzo 3 -folds in , i.e. hypersurfaces of degree defined by a homogeneous polynomial , where are algebraically dependent but linearly independent forms of degree in , and is a form in of degree . Perazzo 3-folds have vanishing hessian and, hence, the associated graded Artinian Gorenstein algebra fails the strong Lefschetz Property. In this paper, we determine the maximum and minimum Hilbert function of and we prove that if has maximal Hilbert function it fails the weak Lefschetz Property while it satisfies the weak Lefschetz Property when it has minimum Hilbert function. In addition, we classify all Perazzo 3 -folds in such that has minimum Hilbert function
Hilbert functions and Jordan type of Perazzo Artinian algebras
No full textWe 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 page
Perazzo 3-folds and the weak Lefschetz property
No full textWe deal with Perazzo 3-folds in P4, i.e. hypersurfaces X = V(f) subset of P4 of degree d defined by a homogeneous polynomial f(x0, x1, x2, u, v) = p0(u, v)x0 +p1(u, v)x1 + p2(u, v)x2 + g(u, v), where p0, p1, p2 are algebraically dependent but linearly independent forms of degree d - 1 in u, v, and g is a form in u, v of degree d. Perazzo 3-folds have vanishing hessian and, hence, the associated graded Artinian Gorenstein algebra Af fails the strong Lefschetz Property. In this paper, we determine the maximum and minimum Hilbert function of Af and we prove that if Af has maximal Hilbert function it fails the weak Lefschetz Property while it satisfies the weak Lefschetz Property when it has minimum Hilbert function. In addition, we classify all Perazzo 3-folds in P4 such that Af has minimum Hilbert function.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/)
Perazzo -folds and the weak Lefschetz property
No full textIn this paper, we determine the maximum and the minimum
of the Hilbert vectors of Perazzo algebras , where is a Perazzo
polynomial of degree in variables. These algebras always fail the
Strong Lefschetz Property. We determine the integers such that
(resp. ) is unimodal, and we prove that always fails
the Weak Lefschetz Property if its Hilbert vector is maximum, while it
satisfies the Weak Lefschetz Property if it is minimum, unimodal, and satisfies
an additional mild condition. We determine the minimal free resolution of
Perazzo algebras associated to Perazzo threefolds in with minimum
Hilbert vectors. Finally we pose some open problems in this context.
Dedicated to Enrique Arrondo on the occasion of his birthday.Comment: 24 pages, to be published in Rendiconti del Circolo Matematico di
Palermo Series
Perazzo hypersurfaces and the Lefschetz properties
No full textTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Rosa M. Miró-Roig[en] The main goal of this writing is to introduce basic concepts of algebraic geometry and commutative algebra to be able to study the relationship between Perazzo hypersurfaces and the Lefschetz properties. We will introduce graded algebras and how to construct one of them from a hypersurface to further check if they satisfy any of the properties. In this paperwork, we have found an upper bound and a low enough value of the Hilbert vector for Perazzo hypersurfaces. The notable result we have obtained is that the Weak Lefschetz property is failed to
obtain when the h-vector is maximal, and conversely, it is always obtained when the h-vector is on that low value
- …
