D-modules: Applications to Algebraic Geometry, Arithmetic and Mirror Symmetry / D-modules: Applications en géométrie algébrique, arithmétique et symétrie miroir

Collection D-modules: Applications to Algebraic Geometry, Arithmetic and Mirror Symmetry / D-modules: Applications en géométrie algébrique, arithmétique et symétrie miroir

Organizer(s) Hertling, Claus ; Sabbah, Claude ; Sevenheck, Christian

Date(s) 11/04/2022 - 15/04/2022

linked URL https://conferences.cirm-math.fr/2320.html

00:00:00 / 00:00:00

5 5

Hodge filtration and birational geometry

I will give a general introduction to the study of the Hodge filtration on local cohomology sheaves associated to closed subschemes of smooth complex varieties, using techniques from both D-module theory and birational geometry. In the case of hypersurfaces, this is essentially the theory of Hodge ideals, which I will recall. This study has applications to various topics, like local vanishing, local cohomological dimension, the Du Bois complex, minimal exponents of singularities, etc. I will discuss a few, and more will appear in M. Mustaja's lecture.

Information about the video

Date of recording 14/04/2022
Date of publication 02/05/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19907303
Cite this video Popa, Mihnea (14/04/2022). Hodge filtration and birational geometry. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19907303
URL https://dx.doi.org/10.24350/CIRM.V.19907303

Domain(s)

Algebraic Geometry

Bibliography

MUSTATA, Mircea et POPA, Mihnea. Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension. arXiv preprint arXiv:2108.05192, 2021. - https://arxiv.org/abs/2108.05192
MUSTAŢĂ, Mircea et POPA, Mihnea. Hodge ideals. Mem. Amer. Math. Soc. 262. 2019. - https://doi.org/10.1090/MEMO/1268

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2320/Slides/popa.pdf

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