English

Divisorial Mori contractions of submaximal length

Algebraic Geometry 2024-11-27 v1

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.

Keywords

Cite

@article{arxiv.2411.17549,
  title  = {Divisorial Mori contractions of submaximal length},
  author = {Bruno Dewer},
  journal= {arXiv preprint arXiv:2411.17549},
  year   = {2024}
}

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17 pages