Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces
Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces
复制标题
固定立方超曲面的（伪）自同构的动态度
DOI：
10.1512/iumj.2013.62.5040
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发表时间：
2012
影响因子：
1.1
通讯作者：
J. Blanc
中科院分区：
文献类型：
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作者：
J. Blanc
我们给出了一种构造任意维有理簇的伪自同构群的方法，它逐点固定p^n的三次超曲面的像.这些群是对合的自由积，并且它们的大多数元素具有动态度<；1.此外，所得到的有理簇的Picard群不大，如果维度至少为3.我们还回答了E.Bedford关于平面上存在不能提升为动态度<；1的自同构的平面的双映射的问题.
We give a way to construct group of pseudo-automorphisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of p^n. These group are free products of involutions, and most of their elements have dynamical degree < 1. Moreover, the Picard group of the varieties obtained is not big, if the dimension is at least 3. We also answer a question of E. Bedford on the existence of birational maps of the plane that cannot be lifted to automorphisms of dynamical degree < 1, even if we compose them with an automorphism of the plane.