## 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 |
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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 |

### Bibliographical note

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.

## ASJC Scopus subject areas

- Algebra and Number Theory