论文标题
光滑仿射四边形$ 3 $ folds的一些有趣的异常形态
Some interesting birational morphisms of smooth affine quadric $3$-folds
论文作者
论文摘要
我们研究了一个平稳仿射四倍的三倍二倍的外本图的家族，{compludemumb}，$ x_1x_1x_4-x_2x_2x_3 = $ constant，这似乎具有一些有趣/意外的字符：周期点严格小于其代数熵。这些地图是$ \ mathbb {c}^4 $保留每个Quadrics上多项式地图的限制。本文中的研究是严格和实验性的混合物，在该研究中，对于实验研究，我们依靠Bertini，这是一个可靠且快速的软件，用于复杂的代数几何形状中昂贵的数值计算。
We study a family of birational maps of smooth affine quadric 3-folds, {over the complex numbers}, of the form $x_1x_4-x_2x_3=$ constant, which seems to have some (among many others) interesting/unexpected characters: a) they are cohomologically hyperbolic, b) their second dynamical degree is an algebraic number but not an algebraic integer, and c) the logarithmic growth of their periodic points is strictly smaller than their algebraic entropy. These maps are restrictions of a polynomial map on $\mathbb{C}^4$ preserving each of the quadrics. The study in this paper is a mixture of rigorous and experimental ones, where for the experimental study we rely on Bertini which is a reliable and fast software for expensive numerical calculations in complex algebraic geometry.
