[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ2 (1002ﾚｽ)
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144(1): １３２人目の素数さん [] 2023/03/08(水)20:56 ID:wlya33oV(3/6)
>>143
Xu Jonsson-Mustata conjecture で下記ヒットです
これ関連かな？
http://www.math.utah.edu/~jliu/Stanford%20talk20210226.pdf
Complements and local singularities in birational geometry Jihao Liu University of Utah Stanford, Feb 26th, 2021
P7
Structure of the talk In this talk, I will introduce the complements theory, a technical yet influential theory in birational geometry introduced by V.V. Shokurov.
I will start talking about the intuition of complements from the study of linear systems in birational geometry.
Then, I will introduce the complements theory and talk about my joint work with J. Han and V.V. Shokurov on a complement conjecture of Shokurov.
After that, I will briefly talk about the applications of the complements theory, especially its applications towards the study on local singularities in birational geometry.
I will also talk about an interesting application in the opposite direction.
In the end, I talk about some open problems.
Without further notice, we work over an algebraically closed field k of characteristic zero, e.g., the field of complex numbers C.
つづく
145: １３２人目の素数さん [] 2023/03/08(水)20:56 ID:wlya33oV(4/6)
>>144
つづき
P88
Applications of the complement theorem Although seemingly technical, our theorem on complements is expected to have many applications.
A special case of our theorem, i.e., Birkar’s theorem on boundedness of complements for pairs with finite rational coefficients, already has applications in many areas:
1 The BBAB theorem (i.e., the boundedness of Fano varieties, BAB conjecture) ([Birkar 16], [Birkar 19]).
2 K-stability theory, e.g. Yau-Tian-Donaldson conjecture ([Y.Liu-Xu-Zhuang 21]), Jonsson-Mustat，?a conjecture, openness of K-semistability, Chi Li’s conjecture on minimizers of the normalized volumes ([Blum-Y.Liu-Xu 19], [Xu 20]).
3 Demailly?Koll´ar’s openness conjecture ([Xu 20])
4 Log Calabi-Yau fibrations ([Birkar 18]).
In the rest of the talk, I will talk about the application of our theorem on complements to the study of local singularities questions.
In this case, Birkar’s result is not strong enough, while our result remains useful
(引用終り)
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