TY - JOUR

T1 - Projective varieties of maximal sectional regularity

AU - Brodmann, Markus

AU - Lee, Wanseok

AU - Park, Euisung

AU - Schenzel, Peter

N1 - Funding Information:
The first named author thanks to the Korea University Seoul, to the Mathematisches Forschungsinstitut Oberwolfach, to the Martin-Luther Universität Halle and to the Deutsche Forschungsgemeinschaft for their hospitality and the financial support provided during the preparation of this work. The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2014R1A1A4A01008404 ). The third and fourth named authors were supported by the NRF-DAAD GEnKO Program ( NRF-2011-0021014 ).
Publisher Copyright:
© 2016 Elsevier B.V.

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.

UR - http://www.scopus.com/inward/record.url?scp=84989923121&partnerID=8YFLogxK

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 -