Projective varieties of maximal sectional regularity

Markus Brodmann, Wanseok Lee, Euisung Park, Peter Schenzel

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study projective varieties X⊂Pr of dimension n≥2, of codimension c≥3 and of degree d≥c+3 that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo–Mumford regularity reg(C) of a general linear curve section is equal to d−c+1, the maximal possible value (see [10]). As one of the main results we classify all varieties of maximal sectional regularity. If X is a variety of maximal sectional regularity, then either (a) it is a divisor on a rational normal (n+1)-fold scroll Y⊂Pn+3 or else (b) there is an n-dimensional linear subspace F⊂Pr such that X∩F⊂F is a hypersurface of degree d−c+1. Moreover, suppose that n=2 or the characteristic of the ground field is zero. Then in case (b) we obtain a precise description of X as a birational linear projection of a rational normal n-fold scroll.

Original languageEnglish
Pages (from-to)98-118
Number of pages21
JournalJournal of Pure and Applied Algebra
Volume221
Issue number1
DOIs
Publication statusPublished - 2017 Jan 1

ASJC Scopus subject areas

  • Algebra and Number Theory

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