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Mathematical Sciences --- Applied Mathematics --- Complex Analysis --- General and Others --- Mathematics --- Fonctions d'une variable complexe --- Functions of complex variables --- Functions of complex variables. --- Periodicals.
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Mathematics --- Boundary value problems --- Problèmes aux limites --- Periodicals --- Périodiques --- Boundary value problems. --- Engineering --- Mathematical Sciences --- General and Others --- Applied Mathematics --- differential equations --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Mathematical analysis
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This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.
Algebraic geometry --- Geometry --- Analytical spaces --- Mathematical analysis --- Mathematics --- landmeetkunde --- analyse (wiskunde) --- complexe veranderlijken --- geometrie --- Algebraic geometry. --- Functions of complex variables. --- Polytopes. --- Projective geometry. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Projective Geometry. --- Geometria algebraica
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Mathematics --- Global analysis (Mathematics) --- Geometry --- Analyse globale (Mathématiques) --- Géométrie --- Periodicals. --- Périodiques --- Analyse globale (Mathématiques) --- Géométrie --- Mathematical Sciences --- Algebraic Geometry --- Calculus --- Differential Geometry --- General and Others --- Graph Theory --- Applied Mathematics --- Mathematical Sciences. --- Graph Theory. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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