Segre's regularity bound for fat point schemes

Uwe Nagel; Bill Trok

doi:10.2422/2036-2145.201702_008

Segre's regularity bound for fat point schemes

Uwe Nagel, Bill Trok

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Motivated by questions in interpolation theory and on linear systems of rational varieties, one is interested in upper bounds for the Castelnuovo- Mumford regularity of arbitrary subschemes of fat points. An optimal upper bound, named after Segre, was conjectured by Trung and, independently, by Fatabbi and Lorenzini. It is shown that this conjecture is true. Furthermore, a generalized regularity bound is established that improves the Segre bound in some cases. Among the arguments is a new partition result for matroids.

Original language	English
Pages (from-to)	217-237
Number of pages	21
Journal	Annali della Scuola normale superiore di Pisa - Classe di scienze
Volume	20
Issue number	1
DOIs	https://doi.org/10.2422/2036-2145.201702_008
State	Published - 2020

Bibliographical note

Funding Information:
The first author was partially supported by Simons Foundation grant #317096.

Publisher Copyright:
© 2020 Scuola Normale Superiore. All rights reserved.

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

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10.2422/2036-2145.201702_008

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Segre's regularity bound for fat point schemes

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