Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908459451023360 |
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| author | Iwai, Masataka Matsumura, Shin-ichi Zhong, Guolei |
| author_facet | Iwai, Masataka Matsumura, Shin-ichi Zhong, Guolei |
| contents | In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved or almost nef. Specifically, we show that such a variety $X$, up to a finite quasi-étale cover, admits a rationally connected fibration $X \to A$ onto an abelian variety $A$. For the proof, we develop the theory of positivity of coherent sheaves on projective varieties. As applications, we establish some relations between the geometric properties and positivity of tangent sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations Iwai, Masataka Matsumura, Shin-ichi Zhong, Guolei Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 14J26, 58A30 In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved or almost nef. Specifically, we show that such a variety $X$, up to a finite quasi-étale cover, admits a rationally connected fibration $X \to A$ onto an abelian variety $A$. For the proof, we develop the theory of positivity of coherent sheaves on projective varieties. As applications, we establish some relations between the geometric properties and positivity of tangent sheaves. |
| title | Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations |
| topic | Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 14J26, 58A30 |
| url | https://arxiv.org/abs/2309.09489 |