论文标题
Gorenstein Fano coindex $ 4 $的Gorenstein Fano品种上的Pluri-fundamental除数的奇异性
Singularities of pluri-fundamental divisors on Gorenstein Fano varieties of coindex $4$
论文作者
论文摘要
让$ x $成为Gorenstein的典范Fano品种coindex $ 4 $和dimension $ n $，$ h $基本除数。假设$ h^0（x，h）\ geq n -2 $。我们证明，线性系统的一般元素$ | MH | $对于任何整数$ m \ geq 1 $都具有最坏的规范奇异性。当$ x $具有终端奇点和$ n \ geq 5 $时，我们表明$ | mh | $的一般元素对于任何整数$ m \ geq 1 $都具有最差的终端奇异性。当$ n = 4 $时，我们给出了Gorenstein Terminal Fano四倍$ x $的示例，使得$ | h | $的一般元素没有终端奇点。
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.
