6 problems

Let $f_0=x^p-y^q$ with $p=kq$, where $k\in\mathbb{N}^*$, and suppose that $q$ is not prime. Write $q=ab$, where $a\geqslant2$ is the smallest prime divisor of $q$. Let…

Let $f_0=x^p-y^q$ with $p=kq$, where $k>1$ and $q$ is prime. For a one-parameter deformation $f_s$ of $f_0$, let $\lambda(f_0)$ denote the jump of the Milnor number and let…

The inequality $(\dagger)$. Is there an example for which

Teissier's conjecture. Invariance of the Milnor number in the family should imply invariance of all sectional Milnor numbers, equivalently invariance of $\mu^*$. This conjecture wa…

Generic Milnor number sequence conjecture.

Generic Milnor number conjecture. For generic homogeneous singularities of degree $d$,