TY - JOUR

T1 - Projective varieties of maximal sectional regularity

AU - Brodmann, Markus

AU - Lee, Wanseok

AU - Park, Euisung

AU - Schenzel, Peter

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2016.05.028

DO - 10.1016/j.jpaa.2016.05.028

M3 - Article

AN - SCOPUS:84989923121

VL - 221

SP - 98

EP - 118

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1

ER -