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.

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.