21/07/12 16:25:19.48 SxwQdsFA.net
>>14
なるほど
蛇足ですが下記
なお、Bogomolovさん、1996"Weak Hironaka theorem"という論文があるみたい
URLﾘﾝｸ(en.wikipedia.org)
Resolution of singularities
For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4.[1]
Contents
3 Resolution of singularities of surfaces
3.5 Hironaka's method
4 Resolution of singularities in higher dimensions
4.3 Hironaka's method
Resolution for schemes and status of the problem
When X is defined over a field of characteristic 0 and is Noetherian, this follows from Hironaka's theorem, and when X has dimension at most 2 it was proved by Lipman.
Choosing centers that are regular subvarieties of X
This method leads to a proof that is relatively simpler to present, compared to Hironaka's original proof, which uses the Hilbert-Samuel function as the measure of how bad singularities are. For example, the proofs in Villamayor (1992), Encinas & Villamayor (1998), Encinas & Hauser (2002), and Kollar (2007) use this idea. However, this method only ensures centers of blowings up that are regular in W.
Bibliography
Bogomolov, Fedor A.; Pantev, Tony G. (1996), "Weak Hironaka theorem", Mathematical Research Letters, 3 (3): 299?307, arXiv:alg-geom/9603019, doi:10.4310/mrl.1996.v3.n3.a1, S2CID 14010069
(Bogomolovさん、前スレ91より)
URLﾘﾝｸ(www.maths.nottingham.ac.uk)
FOUNDATIONS AND PERSPECTIVES OF ANABELIAN GEOMETRY, RIMS WORKSHOP
June 29 2021 20:30-21:30 Fedor Bogomolov Birational geometry and group theory