Irregular threefolds with numerically trivial canonical divisor
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918308635213824 |
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| author | Chen, Jingshan Wang, Chongning Zhang, Lei |
| author_facet | Chen, Jingshan Wang, Chongning Zhang, Lei |
| contents | In this paper, we classify irregular threefolds with numerically trivial canonical divisors in positive characteristic. For such a variety, if its Albanese dimension is not maximal, then the Albanese morphism will induce a fibration which either maps to a curve or is fibered by curves. In practice, we treat arbitrary dimensional irregular varieties with either one dimensional Albanese fiber or one dimensional Albanese image. We prove that such a variety carries another fibration transversal to its Albanese morphism (a "bi-fibration" structure), which is an analog structure of bielliptic or quasi-bielliptic surfaces. In turn, we give an explicit description of irregular threefolds with trivial canonical divisors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irregular threefolds with numerically trivial canonical divisor Chen, Jingshan Wang, Chongning Zhang, Lei Algebraic Geometry 14G17, 14D99, 14J32, 14J10 In this paper, we classify irregular threefolds with numerically trivial canonical divisors in positive characteristic. For such a variety, if its Albanese dimension is not maximal, then the Albanese morphism will induce a fibration which either maps to a curve or is fibered by curves. In practice, we treat arbitrary dimensional irregular varieties with either one dimensional Albanese fiber or one dimensional Albanese image. We prove that such a variety carries another fibration transversal to its Albanese morphism (a "bi-fibration" structure), which is an analog structure of bielliptic or quasi-bielliptic surfaces. In turn, we give an explicit description of irregular threefolds with trivial canonical divisors. |
| title | Irregular threefolds with numerically trivial canonical divisor |
| topic | Algebraic Geometry 14G17, 14D99, 14J32, 14J10 |
| url | https://arxiv.org/abs/2409.19973 |