6 problems

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be reduced holomorphic function-germs, and let $V(f)$ and $V(g)$ denote their zero-set germs at the origin. Suppose there is a home…

Conjecture on numeric invariants. Within this framework, no new numeric invariants exist beyond those already presented, although some combinatorial invariants may arise.

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be reduced holomorphic function-germs. Suppose there is a homeomorphism $\varphi\colon(\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ such tha…

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be holomorphic function-germs, and write $f_*$ and $g_*$ for their initial forms. Suppose there is a homeomorphism…

Let $d_1,d_2>0$ and let $\Omega_{\mathbb{C}^2}(d_1,d_2)$ denote the space of polynomial mappings from $\mathbb{C}^2$ with the indicated degrees. Let $U$ be the set of topologically…

Topological classification conjecture. The two foliation germs are topologically equivalent if and only if: (1) the ray configurations of their eigenvalue tuples are equivalent; an…