3 problems

Machado–Seade conjecture. The following statements are equivalent: $(D,0)$ is weighted homogeneous; there exists a holomorphic vector field tangent to $D$ with an isolated singular…

Let $m,i\in\mathbb{Z}_{\geq 0}$, and let $\widetilde{f_i^m}(x,y)$ be the deformed polynomial defined from the coefficients of … For a polynomial $g$, write $g\in((x+y+m)_{2m+1})$ w…

Terao-type conjecture. The invariant $\nu(C)$ is combinatorially determined.