自同态的全不变超曲面的奇点
Singularities of totally invariant hypersurfaces of endomorphisms
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中文总结 AI 辅助
本文证明复射影流形极化自同态的全不变超曲面的奇点轨迹各分支余维数为一，并由此推出$\mathbb P^4$上全不变除子的线性性。
中文摘要 AI 辅助
设$f\colon X\to X$为复射影流形的极化自同态，且$D\subset X$为约化全不变超曲面。我们证明了$D$的奇点轨迹的每个不可约分支在$D$中的余维数为一。特别地，若$D$是正规的，则它是光滑的。作为应用，我们证明了$\mathbb P^4$上自同态的全不变除子的线性性。
英文摘要
Let $f\colon X\to X$ be a polarised endomorphism of a complex projective manifold, and let $D\subset X$ be a reduced totally invariant hypersurface. We prove that every irreducible component of the singular locus of $D$ has codimension one in $D$. In particular, if $D$ is normal, then it is smooth. As an application we prove the linearity of totally invariant divisors for endomorphisms of $\mathbb P^4$.
