On -modules related to the -function and Hamiltonian flow
On -modules related to the -function and Hamiltonian flow
Let $f$ be a quasi-homogeneous polynomial with an isolated singularity in $\mathbf{C}^{n}$ . We compute the length of the ${\mathcal{D}}$ -modules ${\mathcal{D}}f^{\unicode[STIX]{x1D706}}/{\mathcal{D}}f^{\unicode[STIX]{x1D706}+1}$ generated by complex powers of $f$ in terms of the Hodge filtration on the top cohomology of the Milnor fiber. When $\unicode[STIX]{x1D706}=-1$ we obtain one more than the …