论文标题
Bi-Lipschitz多样性的不变性
Bi-Lipschitz invariance of the multiplicity
论文作者
论文摘要
该曲线上以$ p $的点为$ p $的代数曲线$ c $的多样性定义为与$ c $相交的点数与一条通用复杂线路的多个点数，该点通过一条通向点$ p $的通用复合线。结果表明，$ p $是曲线$ c $的一个单数点，并且只有当此多重性大于或等于2时，从这个意义上讲，这样的整数数字可以视为如何衡量奇数可以是曲线$ c $的点。在这些注释中，我们解决了复杂代数集的奇异点的多样性的经典概念（不一定是复杂的曲线），并且从多重性构想的角度来看，奇异点的多样性的本质是几何不变的（Zariski 1971）。更确切地说，我们对与Lev Birbrair，JavierFernándezDeBobadilla，LêdungDung Trang和Mikhail verbitsky共同获得的结果进行了讨论。
The multiplicity of an algebraic curve $C$ in the complex plane at a point $p$ on that curve is defined as the number of points that occur at the intersection of $C$ with a general complex line that passes close to the point $p$. It is shown that $p$ is a singular point of the curve $C$ if and only if this multiplicity is greater than or equal to 2, in this sense, such an integer number can be considered as a measure of how singular can be a point of the curve $C$. In these notes, we address the classical concept of multiplicity of singular points of complex algebraic sets (not necessarily complex curves) and we approach the nature of the multiplicity of singular points as a geometric invariant from the perspective of the Multiplicity Conjecture (Zariski 1971). More precisely, we bring a discussion on the recent results obtained jointly with Lev Birbrair, Javier Fernández de Bobadilla, Lê Dung Trang and Mikhail Verbitsky on the bi-Lipschitz invariance of the multiplicity.
