Bøger af Ivan Cheltsov

This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and PohangThe conferences were focused on the following two related problems:¿ existence of Kähler¿Einstein metrics on Fano varieties¿ degenerations of Fano varietieson 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¿YaüDonaldson 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.

This work focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The authors present interesting results that highlight the beauty of icosahedral symmetries of the variety V5. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity.