Let $Z\subset{ \bf P}^{ n-1}$ be a hypersurface such that the associated reduced hypersurface $Z_{ \rm red}$ has only weighted homogeneous isolated singularities. In the case $Z$ is a reduced curve or $Z_{ \rm red}$ has only homogeneous isolated singularities with $n$ at least $4$, we show that the strong monodromy conjecture for a defining polynomial $f$ of $Z$ follows immediately from arxiv:1609.04801v1 using in the reduced curve case a formula of Denef and Loeser for Newton-nondegenerate polynomials of three variables (which can be deduced in the applied case from the one for the two variable case) together with known results about the strong monodromy conjecture in the two variable case. Here an amazing cancellation occurs so that possible counterexamples fail.
Categories: math.AG