8 papers
Moduli of atoms of complex projective varieties
Maxim Kontsevich, Szilard Szabo
The category of constituent pieces of Dubrovin connection of varieties is introduced and shown to be representable in affine space.
Burnside rings and volume forms with logarithmic poles
Antoine Chambert-Loir, Maxim Kontsevich, Yuri Tschinkel
We develop a theory of Burnside rings in the context of birational equivalences of algebraic varieties equipped with logarithmic volume forms. We introduce a residue homomorphism a…
Atoms meet symbols
Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich
This paper introduces a novel framework for constructing invariants in -equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed…
Birational Invariants from Hodge Structures and Quantum Multiplication
Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev +1
We introduce new invariants of smooth complex projective varieties, called Hodge atoms. Their construction combines rational Gromov-Witten invariants with classical Hodge theory an…
Non-commutative cluster Lagrangians
Alexander B. Goncharov, Maxim Kontsevich
The space Loc(m,S) of rank m flat bundles on a closed surface S is K_2-symplectic. A threefold M bounding S gives rise a K_2-Lagrangian in Loc(m,S) given by the flat bundles on S e…
Explicit formulas for arithmetic support of differential and difference operators
Maxim Kontsevich, Alexander Odesskii
We compute arithmetic support of the formal deformations of the differential operator , where $r_1,...,r_k\in\mathbb{…