Divisorial Mori contractions of submaximal length
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916496722100224 |
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| author | Dewer, Bruno |
| author_facet | Dewer, Bruno |
| contents | A result due to Cho, Miyaoka, Shepherd-Barron [CMSB] and Kebekus [Ke] provides a numerical characterization of projective spaces. More recently, Dedieu and Höring [DH] gave a characterization of smooth quadrics based on similar arguments. As a relative version of [CMSB] and [Ke], Höring 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Divisorial Mori contractions of submaximal length Dewer, Bruno Algebraic Geometry 14E30 (Primary) 14E05, 14D06 (Secondary) A result due to Cho, Miyaoka, Shepherd-Barron [CMSB] and Kebekus [Ke] provides a numerical characterization of projective spaces. More recently, Dedieu and Höring [DH] gave a characterization of smooth quadrics based on similar arguments. As a relative version of [CMSB] and [Ke], Höring 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. |
| title | Divisorial Mori contractions of submaximal length |
| topic | Algebraic Geometry 14E30 (Primary) 14E05, 14D06 (Secondary) |
| url | https://arxiv.org/abs/2411.17549 |