Hodge filtrations for twisted parametrically prime divisors

TL;DR

This paper extends the theory of Hodge filtrations to $Q$-divisors, providing explicit formulas for the filtration on modules associated with parametrically prime holomorphic functions, enhancing understanding of their algebraic and geometric properties.

Contribution

It introduces explicit expressions for Hodge filtrations on modules related to $Q$-divisors and parametrically prime functions, expanding previous work to a broader class of divisors.

Findings

Explicit formula for Hodge filtration on $Q$-divisors

Extension of previous results to more general divisors

Enhanced understanding of algebraic structure of modules

Abstract

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