Minimal projective varieties satisfying Miyaoka's equality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917030852034560 |
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| author | Iwai, Masataka Matsumura, Shin-ichi Müller, Niklas |
| author_facet | Iwai, Masataka Matsumura, Shin-ichi Müller, Niklas |
| contents | In this paper, we establish a structure theorem for minimal projective klt varieties $X$ that satisfiy Miyaoka's equality $3c_2(X) = c_1(X)^2$. Specifically, we prove that the canonical divisor $K_X$ is semi-ample and that the Kodaira dimension $κ(K_X)$ is either $0$, $1$, or $2$. Furthermore, based on this abundance result, we show that a maximally quasi-étale cover of $X$ is smooth, and we describe explicitly the structure of the Iitaka fibration. Additionally, we prove a similar result for projective klt varieties with a nef anti-canonical divisor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_07568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal projective varieties satisfying Miyaoka's equality Iwai, Masataka Matsumura, Shin-ichi Müller, Niklas Algebraic Geometry Complex Variables Differential Geometry Primary 14E30, Secondary 14D06, 32Q26, 32Q30 In this paper, we establish a structure theorem for minimal projective klt varieties $X$ that satisfiy Miyaoka's equality $3c_2(X) = c_1(X)^2$. Specifically, we prove that the canonical divisor $K_X$ is semi-ample and that the Kodaira dimension $κ(K_X)$ is either $0$, $1$, or $2$. Furthermore, based on this abundance result, we show that a maximally quasi-étale cover of $X$ is smooth, and we describe explicitly the structure of the Iitaka fibration. Additionally, we prove a similar result for projective klt varieties with a nef anti-canonical divisor. |
| title | Minimal projective varieties satisfying Miyaoka's equality |
| topic | Algebraic Geometry Complex Variables Differential Geometry Primary 14E30, Secondary 14D06, 32Q26, 32Q30 |
| url | https://arxiv.org/abs/2404.07568 |