Projective varieties of maximal sectional regularity

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• 作者：Markus Brodmann^a ; ^{brodmann@math.unizh.ch" class="auth_mail" title="E-mail the corresponding author} ; Wanseok Lee^b ; ^{wslee@pknu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Euisung Park^c ; ^{euisungpark@korea.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Peter Schenzel^d ; ^{schenzel@informatik.uni-halle.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 14H45 ; 13D02
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：221
• 期：1
• 页码：98-118
• 全文大小：497 K

文摘

We study projective varieties acf9b344946e8eb1136d79ac" title="Click to view the MathML source">X⊂P^r$X\subset {\mathbb{P}}^r$ of dimension n≥2$n\ge 2$, of codimension acdc8f4d76dc650fb71" title="Click to view the MathML source">c≥3$c\ge 3$ and of degree d≥c+3$d\ge c+3$ that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo–Mumford regularity reg(C)$\mathrm{reg}(\mathcal{C})$ of a general linear curve section is equal to d−c+1$d-c+1$, 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)$(n+1)$-fold scroll aca25f3d06da1a85f7" title="Click to view the MathML source">Y⊂Pⁿ⁺³$Y\subset {\mathbb{P}}^{n+3}$ or else (b) there is an n  -dimensional linear subspace F⊂P^r$\mathbb{F}\subset {\mathbb{P}}^r$ such that X∩F⊂F$X\cap \mathbb{F}\subset \mathbb{F}$ is a hypersurface of degree d−c+1$d-c+1$. Moreover, suppose that n=2$n=2$ 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.