On zero-dimensional subschemes of a complete intersections.
Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute bounds on the maximal order type.
Partial intersections and graded Betti numbers.
Quadrics through a set of points and their syzygies.
Resolutions of generic points lying on a smooth quadric.
Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.
In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.
Série de Poincaré pour certaines courbes
Some conjectures about the Hilbert series of generic ideals in the exterior algebra.
Some defective secant varieties to osculating varieties of Veronese surfaces.
We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Osk,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.
Standard monmials of some symmetric sets.
Stretched -primary ideals.
Sugli ideali di Borel
In this note we study some algebraic properties of Borel Ideals in the ring of polynomials over an effective field of characteristic zero by using a suitable partial order relation defined on the set of terms of each degree. In particular, in the three variable case, we characterize all the 0-dimensional Borel ideals corresponding to an admissible -vector and their minimal free resolutions.
Sur les invariants des pinceaux de formes quintiques binaires
On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.
Symmetry Groups in the Alhambra
The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The cones associated to some tranversal polymatroids.
The connection between a conjecture of Carlisle and Kropholler, now a theorem of Benson and Crowley-Boevey, and Grothendieck's Riemannian-Roch and duality theorems.
The finite free extension of artinian -algebras with the strong Lefschetz property
The Hilbert scheme of space curves of small diameter
This paper studies space curves of degree and arithmetic genus , with homogeneous ideal and Rao module , whose main results deal with curves which satisfy (e.g. of diameter, ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, , at under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of turns out to be equivalent to the...
Théorème de Hilbert-Samuel «arithmétique»
On donne une nouvelle démonstration directe du théorème de Hilbert-Samuel arithmétique et on déduit un critère numérique pour l’existence de sections d’un fibré en droite sur une variété arithmétique de norme sup inférieure à un.