Arithmetic and Algebraic Geometry

This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023. Manin was one of the giants of modern mathematics. His work covered a wide range of fields, including logic, number theory, geometry, mathematical physics, theoretical computer science, and linguistics. The contributions collected here are on topics close to his life-long passion: arithmetic and algebraic geometry.

Combines high-level and survey research on algebraic and arithmetic geometry Compiles key research by students of Manin that continue his legacy Highlights developments in research related to Manin, including toric geometry and representation theory

Auteur

Yuri Tschinkel's research is at the interface of algebraic geometry and number theory. He studies higher-dimensional algebraic varieties, their hidden symmetries and rational points. He is the author of 160 papers and editor of 20 books. He is a Fellow of the American Mathematical Society and of the American Association for the Advancement of Science. He is a member of Leopoldina, the German National Academy of Sciences, and a Foreign Member of Academia Europaea.

Contenu

Preface.- Projecting lattice polytopes according to the Minimal Model Program.- Zeta-polynomials, superpolynomials, DAHA and plane curve singularities.- Rational points over C1 fields.- On isomorphisms of ind-varieties of generalized flags.- Spectral description of non-commutative local systems on surfaces and non-commutative cluster varieties.- Semi-stable reduction of foliations.- The Hasse principle for 9-nodal cubic 3-folds.- Manin's work in birational geometry.- Endomorphism Algebras and Automorphism Groups of certain Complex Tori.