2018/10/15 by Mingyi Zhang, Zhang, Mingyi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.AG #msc:14F10 #msc:14J17 #msc:32S25
paper · pdf · doi:10.48550/arxiv.1810.06656
23 pages; add an assumption in the nondegenerate case that f need to be convenient; add Lemma 5.3 and add a proof of Lemma 5.4
arxiv created 2019/01/30 · arxiv updated 2019/01/31
We give an explicit formula for the Hodge filtration on the \mathscrDX-module OX(*Z)f1-α associated to the effective ℚ-divisor D=α⋅ Z, where 0<α≤1 and Z=(f=0) is an irreducible hypersurface defined by f, a weighted homogeneous polynomial with an isolated singularity at the origin. In particular this gives a formula for the Hodge ideals of D. We deduce a formula for the generating level of the Hodge filtration, as well as further properties of Hodge ideals in this setting. We also extend the main theorem to the case when f is a germ of holomorphic function that is convenient and has non-degenerate Newton boundary.