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arXiv · 2308.10440

Kawamata--Miyaoka type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities

Haidong Liu·Jie Liu
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Abstract

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.

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Haidong Liu, Jie Liu. 2023-08-21. Kawamata--Miyaoka type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities. https://arxiv.org/abs/2308.10440

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