Hodge filtrations for twisted parametrically prime divisors

Abstract

We extend previous work to the case of $\mathbb{Q}$-divisors. Namely, for certain parametrically prime holomorphic functions $f$ and $\hat{I}\pm \ge 0$, we obtain an explicit expression for the Hodge filtration on $\mathcal{M}(f^{-\hat{I}\pm }):={\mathcal{O}}_X(\ast f)f^{-\hat{I}\pm }$.