Бирациональные автоморфизмы многообразий Кузнецова Александра Александровна

Короткий опис

Кузнецова, Александра Александровна.
Бирациональные автоморфизмы многообразий = Birational automorphisms of varieties : Birational automorphisms of varieties : диссертация ... кандидата физико-математических наук : 01.01.06 / Александра Александровна Кузнецова; [Место защиты: ФГАОУ ВО «Национальный исследовательский университет «Высшая школа экономики»]. - Париж, 2022. - 118 с. : ил.
Оглавление диссертациикандидат наук Кузнецова Александра Александровна
Contents
Introduction
1 Finite groups of automorphisms
1.1 Introduction
1.2 Preliminaries
1.2.1 Finite groups
1.2.2 3-subgroups in GLn(C) and PGLn(C)
1.2.3 Group action on algebraic varieties
1.2.4 Examples
1.2.5 p-Jordan property
1.2.6 Fano threefolds
1.3 Automorphisms of quasi-projective surfaces
1.3.1 Automorphisms of open subsets of E x P1
1.3.2 Proof of Theorem
1.4 Automorphisms of 3-dimensional Mori fiber spaces
1.4.1 Singular Fano threefolds
1.4.2 Fano threefolds with p >
1.4.3 Fano threefolds with p =1
1.4.4 Proof of Theorem
2 Regularization of birational automorphisms
2.1 Introduction
2.2 Preliminaries
2.2.1 Birational maps acting on the divisor class group
2.2.2 A special construction of a flop
2.2.3 Dynamical degrees
2.2.4 Example
2.3 Proof of Theorem
2.3.1 Regularizations
2.3.2 Fibrations over surfaces
2.4 Blanc's pseudo-automorphism
2.4.1 Construction of a pseudo-automorphism
2.4.2 Formulas for involutions
2.4.3 Composition of three involutions
2.4.4 Sage computations for Lemma
2.4.5 Proof of Theorem
3 Automorphisms of Bogomolov—Guan manifolds
3.1 Introduction
3.2 Preliminaries
3.2.1 Holomorphic symplectic manifolds
3.2.2 Complex spaces and meromorphic maps
3.3 Non-Kahler holomorphic symplectic manifolds
3.3.1 Kodaira surfaces
3.3.2 Bogomolov-Guan example
3.3.3 The algebraic reduction of BG-manifolds
3.4 Submanifolds in BG-manifolds
3.4.1 Kodaira-type manifolds
3.4.2 Submanifolds in Sn/F
3.4.3 Fibers of $ and n
3.4.4 Proof of Theorem
3.5 Automorphisms of BG-manifolds
3.5.1 Divisor D as a dual variety
3.5.2 Regular automorphisms of a BG-manifold
3.5.3 Bimeromorphic automorphisms of a BG-fourfold
Conclusion
Bibliography