2025/03/18 by Dakin, Henry
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.14216
We study the canonical mixed Hodge module structure associated to the \mathscrDX-module \mathscrM(f-α):=\mathscrOX(*f)f-α. We particularly focus on the weight filtration and extend many known results to the weighted setting. We obtain new relations between Hodge theory and birational geometry. We derive a general formula for the Hodge and weight filtrations on \mathscrM(f-α), and use this to obtain results concerning the largest weight of \mathscrM(f-α) and the generating level of weight filtration steps. Finally, we obtain expressions for several classes of divisor, including certain parametrically prime divisors.