Projective varieties of maximal sectional regularity
- Authors
- Brodmann, Markus; Lee, Wanseok; Park, Euisung; Schenzel, Peter
- Issue Date
- 1월-2017
- Publisher
- ELSEVIER SCIENCE BV
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, v.221, no.1, pp.98 - 118
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PURE AND APPLIED ALGEBRA
- Volume
- 221
- Number
- 1
- Start Page
- 98
- End Page
- 118
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/85146
- DOI
- 10.1016/j.jpaa.2016.05.028
- ISSN
- 0022-4049
- Abstract
- We study projective varieties X subset of 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 subset of Pn+3 or else (b) there is an n-dimensional linear subspace F subset of P-r such that X boolean AND F subset of 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. (C) 2016 Elsevier B.V. All rights reserved.
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