Noncommutative resolution, F-blowups and D-modules

Yukinobu Toda; Takehiko Yasuda

doi:10.1016/j.aim.2009.04.004

Noncommutative resolution, F-blowups and D-modules

Yukinobu Toda, Takehiko Yasuda

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.

Original language	English
Pages (from-to)	318-330
Number of pages	13
Journal	Advances in Mathematics
Volume	222
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2009.04.004
Publication status	Published - 2009 Sep 10

Keywords

D-module
F-blowup
Noncommutative resolution
Positive characteristic
Singularity

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2009.04.004

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abstract = "We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.",

keywords = "D-module, F-blowup, Noncommutative resolution, Positive characteristic, Singularity",

author = "Yukinobu Toda and Takehiko Yasuda",

note = "Funding Information: This work was supported by Grant-in-Aid for Young Scientists (Start-up) (20840036, 20503882) and World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. The second author thanks Shoji Yokura for his help in reading a paper written in German.",

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AU - Yasuda, Takehiko

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N2 - We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.

AB - We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.

KW - D-module

KW - F-blowup

KW - Noncommutative resolution

KW - Positive characteristic

KW - Singularity

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Noncommutative resolution, F-blowups and D-modules

Abstract

Keywords

ASJC Scopus subject areas

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