Kawamata--Miyaoka type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915036734160896 |
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| author | Liu, Haidong Liu, Jie |
| author_facet | Liu, Haidong Liu, Jie |
| contents | Let $X$ be an $n$-dimensional normal $\mathbb{Q}$-factorial projective variety with canonical singularities and Picard number one such that $X$ is smooth in codimension two, $-K_X$ is ample and $n\geq 2$. We prove that $X$ satisfies the following Kawamata--Miyaoka type inequality: \[ c_1(X)^n< 4 c_2(X)\cdot c_1(X)^{n-2}. \] If additionally $X$ is a threefold with terminal singularities, then a stronger inequality is also obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10440 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kawamata--Miyaoka type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities Liu, Haidong Liu, Jie Algebraic Geometry 14J45, 14J10, 14J30 Let $X$ be an $n$-dimensional normal $\mathbb{Q}$-factorial projective variety with canonical singularities and Picard number one such that $X$ is smooth in codimension two, $-K_X$ is ample and $n\geq 2$. We prove that $X$ satisfies the following Kawamata--Miyaoka type inequality: \[ c_1(X)^n< 4 c_2(X)\cdot c_1(X)^{n-2}. \] If additionally $X$ is a threefold with terminal singularities, then a stronger inequality is also obtained. |
| title | Kawamata--Miyaoka type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities |
| topic | Algebraic Geometry 14J45, 14J10, 14J30 |
| url | https://arxiv.org/abs/2308.10440 |