Hodge Ideals

By M. Mustaţă, Mihnea Cristian Popa. Memoirs of the American Mathematical Society, 2016

57 citations recorded by the source corpus.

We use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. We analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.

Subfields: Algebra and Number Theory, Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ddf270b472d78b0b6185471beede0315e3de43ed

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Mihnea Cristian Popa
2. M. Mustaţă
3. Chi Li
4. Mattias Jonsson
5. H. Blum
6. Yuchen Liu
7. Sam Payne
8. Kiumars Kaveh

In Computational Mechanics

1. Mihnea Cristian Popa
2. M. Mustaţă

In Geometry and Topology

1. Mihnea Cristian Popa
2. M. Mustaţă
3. Chi Li
4. S. Ishii
5. H. Blum
6. Mattias Jonsson
7. Kiumars Kaveh
8. Steven Dale Cutkosky

Citations in the corpus

• Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension (2021, methodology): “We also obtain local vanishing results for sheaves of forms with log poles associated to such a resolution, generalising Nakano-type results in [52] and [36].”
• HODGE IDEALS FOR $\mathbb{Q}$-DIVISORS, $V$-FILTRATION, AND MINIMAL EXPONENT (2018, unknown): “If Z is a reduced effective divisor on the smooth variety X and α is a rational number in ( 0 , 1 ] , do we have the inclusion For α = 1, a positive answer is provided by [ MP19a , Theorem C].”