### Abstract

We study projective varieties X⊂P^{r} 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⊂P^{n+3} or else (b) there is an n-dimensional linear subspace F⊂P^{r} 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 language | English |
---|---|

Pages (from-to) | 98-118 |

Number of pages | 21 |

Journal | Journal of Pure and Applied Algebra |

Volume | 221 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*221*(1), 98-118. https://doi.org/10.1016/j.jpaa.2016.05.028

**Projective varieties of maximal sectional regularity.** / Brodmann, Markus; Lee, Wanseok; Park, Euisung; Schenzel, Peter.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 221, no. 1, pp. 98-118. https://doi.org/10.1016/j.jpaa.2016.05.028

}

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.

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

UR - http://www.scopus.com/inward/citedby.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 -