Ivan Cheltsov's Books

Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler–Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler–Einstein metric, containing many additional relevant results such as the classification of all Kähler–Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.

Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. 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.The a

The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.

Book's by Ivan Cheltsov

The Calabi Problem for Fano Threefolds

The Calabi Problem for Fano Threefolds

Cremona Groups and the Icosahedron

Cremona Groups and the Icosahedron

Birationally Rigid Fano Threefold Hypersurfaces

Birationally Rigid Fano Threefold Hypersurfaces

The Calabi Problem for Fano Threefolds

The Calabi Problem for Fano Threefolds

Cremona Groups and the Icosahedron

Cremona Groups and the Icosahedron

Birationally Rigid Fano Threefold Hypersurfaces

Birationally Rigid Fano Threefold Hypersurfaces

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