Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Computing limit linear series with infinitesimal methods

Abstract : 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 which approach a divisor. On the other hand, Nagata in connection with its counter example to the fourteenth problem of Hilbert determined the Hilbert function H(d) of the union of k^2 points of the same multiplicity m in the plane up to degree d=km. We introduce a new method to determine limits of linear systems. This generalizes the result by Alexander and Hirschowitz. Our main application of this method is the conclusion of the work initiated by Nagata: we compute H(d) for all d. As a second application, we determine the generic successive collision of four fat points of the same multiplicity in the plane.
Complete list of metadatas

Cited literature [11 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00002186
Contributor : Laurent Evain <>
Submitted on : Thursday, July 8, 2004 - 5:14:41 PM
Last modification on : Monday, March 9, 2020 - 6:15:52 PM
Document(s) archivé(s) le : Monday, March 29, 2010 - 9:22:23 PM

Identifiers

Collections

Citation

Laurent Evain. Computing limit linear series with infinitesimal methods. 2004. ⟨hal-00002186⟩

Share

Metrics

Record views

282

Files downloads

161