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arXiv · 2206.00881

Singularities of pluri-fundamental divisors on Gorenstein Fano varieties of coindex $4$

Jinhyung Park
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Abstract

Let $X$ be a Gorenstein canonical Fano variety of coindex $4$ and dimension $n$ with $H$ fundamental divisor. Assume $h^0(X, H) \geq n -2$. We prove that a general element of the linear system $|mH|$ has at worst canonical singularities for any integer $m \geq 1$. When $X$ has terminal singularities and $n \geq 5$, we show that a general element of $|mH|$ has at worst terminal singularities for any integer $m \geq 1$. When $n=4$, we give an example of Gorenstein terminal Fano fourfold $X$ such that a general element of $|H|$ does not have terminal singularities.

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Jinhyung Park. 2022-06-02. Singularities of pluri-fundamental divisors on Gorenstein Fano varieties of coindex $4$. https://arxiv.org/abs/2206.00881

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