一个推广的透镜方程的根及其应用
On the roots of an extended lens equation and an application
摘要：
考虑一个混合多项式，它是一个推广的Lens方程$L_{n,m}=\bar z^m-p(z)/q(z)$，其中$\text{degree}\, q=n$，$\text{degree}\, p<n$的分子是一个$(n+m;n,m)$次混合多项式.然后考虑它的$L_{n,m}+ε/z^m$型变形，构造了一个特殊的具有$5n$零点的$(n+2m;n+m,m)$次混合多项式.这概括了Rhie的一个例子。本文给出了原点具有孤立奇点的二元强混合加权齐次多项式模空间连通分支数的一个应用。
英文摘要：
We consider a certain mixed polynomial which is an extended Lens equation $L_{n,m}=\bar z^m-p(z)/q(z)$ with $\text{degree}\, q=n$, $\text{degree}\, p<n$ whose numerator is a mixed polynomial of degree $(n+m;n,m)$. Then we consider its deformation of type $L_{n,m}+ε/z^m$ to construct a special mixed polynomial of degree $(n+2m;n+m,m)$ with $5n$ zeros. This generalizes an example of Rhie. We give an application to the number of connected components of the moduli space of strongly mixed weighted homogeneous polynomials of two variables with isolated singularity at the origin.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
