论文标题
有限形态的界限到具有大型Fano索引的Fano歧管
Boundedness of finite morphisms onto Fano manifolds with large Fano index
论文作者
论文摘要
让$ f：y \ to x $是fano流形$ y $和$ x $之间的有限形态，使得$ x $的fano索引大于1。当$ x $和$ y $都是Picard数字的四倍时，我们表明$ f $的$ f $是$ x $ $ $ $ $ $ $ $ $ $ $ $ $的，bean d $ $ $;因此，这样的$ x $不承认任何非同构透明性内态性。另一方面，当$ x = y $是四倍或del pezzo歧管时，我们证明，如果$ f $是一种int amplified的内态性，则$ x $是折叠的。此外，我们对所有承认非同态内态的奇异四元素进行了分类。
Let $f:Y\to X$ be a finite morphism between Fano manifolds $Y$ and $X$ such that the Fano index of $X$ is greater than 1. On the one hand, when both $X$ and $Y$ are fourfolds of Picard number 1, we show that the degree of $f$ is bounded in terms of $X$ and $Y$ unless $X\cong\mathbb{P}^4$; hence, such $X$ does not admit any non-isomorphic surjective endomorphism. On the other hand, when $X=Y$ is either a fourfold or a del Pezzo manifold, we prove that, if $f$ is an int-amplified endomorphism, then $X$ is toric. Moreover, we classify all the singular quadrics admitting non-isomorphic endomorphisms.
