论文标题
分解为二维和变种环的中心
Factorization centers in dimension two and the Grothendieck ring of varieties
论文作者
论文摘要
我们启动了Birational图的因子化中心的研究，并在本文中的完美领域完成了表面。我们证明，对于每一个男子式的自动形态$ ϕ：x \ dashrightArrow x $ of Perfect Field $ k $上的光滑的投射表面$ x $，爆炸中心在每一个弱分解$ ϕ $的情况下对井口中心都是同构的。这意味着不能基于表面的生育自动形态构建$ 0 $二维品种的非平凡的L等价性。这也意味着，对于每个理性的表面$ x $，理性中心的定义都很好，即存在$ 0 $二维的固有到$ x $，这在任何合理性构建$ x $中都被炸毁。
We initiate the study of factorization centers of birational maps, and complete it for surfaces over a perfect field in this article. We prove that for every birational automorphism $ϕ: X \dashrightarrow X$ of a smooth projective surface $X$ over a perfect field $k$, the blowup centers are isomorphic to the blowdown centers in every weak factorization of $ϕ$. This implies that nontrivial L-equivalences of $0$-dimensional varieties cannot be constructed based on birational automorphisms of a surface. It also implies that rationality centers are well-defined for every rational surface $X$, namely there exists a $0$-dimensional variety intrinsic to $X$, which is blown up in any rationality construction of $X$.
