论文标题
耗尽功能和正常形式的适当地图
Exhaustion functions and normal forms for proper maps of balls
论文作者
论文摘要
我们研究了在不同维度上球的合理正确地图与该地图引起的单位球的强烈多毛缩减功能之间的关系。将这种耗尽功能的独特临界点放在原点上导致正常形式，用于合理的适当地图。地图的正常形式由单位型组成，将原点归于原点，并通过消除线性项并对角线化二次部分来使分母归一化。分母的二次部分的奇异值是地图的球形不变性。当这些奇异值是积极且独特的时，正态形式被确定为单位群的有限亚组。我们还研究了哪种分母用于立方图，而当我们不需要将起源驱动到起源时，哪些图等于多项式。
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at the origin leads to a normal form for rational proper maps of balls. The normal form of the map, which is up to composition with unitaries, takes the origin to the origin, and it normalizes the denominator by eliminating the linear terms and diagonalizing the quadratic part. The singular values of the quadratic part of the denominator are spherical invariants of the map. When these singular values are positive and distinct, the normal form is determined up to a finite subgroup of the unitary group. We also study which denominators arise for cubic maps, and when we do not require taking the origin to the origin, which maps are equivalent to polynomials.
