Page 1 Next

Displaying 1 – 20 of 82

Showing per page

3-dimensional sundials

Enrico Carlini, Maria Catalisano, Anthony Geramita (2011)

Open Mathematics

R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

Bounds on multisecant lines.

Scott Nollet (1998)

Collectanea Mathematica

The purpose of this paper is twofold. First, we give an upper bound on the order of a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we give an explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine a standard linking theorem. These results are tied together by the construction of sharp examples for the bound,...

Caractères numériques et fonctions de Macaulay.

Mireille Martin-Deschamps (2004)

Collectanea Mathematica

The postulation of Aritméticamente Cohen-Macaulay (ACM) subschemes of the projective space PkN is well known in the case of codimension 2. There are many different ways of recording this numerical information: numerical character of Gruson/Peskine, h-vector, postulation character of Martin-Deschamps/Perrin... The first aim of this paper is to show the equivalence of these notions. The second and most important aim, is to study the postulation of codimension 3 ACM subschemes of PN. We use a result...

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...

Currently displaying 1 – 20 of 82

Page 1 Next