Kovács' conjecture on characterization of projective space and hyperquadrics
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914292806189056 |
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| author | Ghosh, Soham |
| author_facet | Ghosh, Soham |
| contents | We prove Kovács' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization involving symmetric powers instead of exterior powers. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wiśniewski, Kobayashi-Ochiai, and Araujo-Druel-Kovács type characterizations of such varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kovács' conjecture on characterization of projective space and hyperquadrics Ghosh, Soham Algebraic Geometry 14M20, 14J45 We prove Kovács' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization involving symmetric powers instead of exterior powers. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wiśniewski, Kobayashi-Ochiai, and Araujo-Druel-Kovács type characterizations of such varieties. |
| title | Kovács' conjecture on characterization of projective space and hyperquadrics |
| topic | Algebraic Geometry 14M20, 14J45 |
| url | https://arxiv.org/abs/2601.10055 |