Divisorial Mori contractions of submaximal length
Abstract
A result due to Cho, Miyaoka, Shepherd-Barron [CMSB] and Kebekus [Ke] provides a numerical characterization of projective spaces. More recently, Dedieu and H\"oring [DH] gave a characterization of smooth quadrics based on similar arguments. As a relative version of [CMSB] and [Ke], H\"oring and Novelli proved in [HN] that the locus covered by positive-dimensional fibres in a Mori contraction of maximal length is a projective bundle up to birational modification. We change the length hypothesis and we prove that the exceptional locus of a divisorial Mori contraction of submaximal length is birational either to a projective bundle, or to a quadric bundle.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.