文摘
We study projective varieties 9b344946e8eb1136d79ac" title="Click to view the MathML source">X⊂Pr of dimension n≥2, of codimension bee5b37acdc8f4d76dc650fb71" title="Click to view the MathML source">c≥3 and of degree d≥c+3 that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo–Mumford regularity a191" title="Click to view the MathML source">reg(C) of a general linear curve section is equal to 9eb4cc4" title="Click to view the MathML source">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 e915" title="Click to view the MathML source">(n+1)-fold scroll 9e6818d34824aca25f3d06da1a85f7" title="Click to view the MathML source">Y⊂Pn+3 or else (b) there is an n -dimensional linear subspace e9134c536eb2702627e07ee91e9be614" title="Click to view the MathML source">F⊂Pr such that e53fef6da26e" title="Click to view the MathML source">X∩F⊂F is a hypersurface of degree 9eb4cc4" title="Click to view the MathML source">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.