activity
20242026
collaborators

8 papers

math.AG2026

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.

math.AG2026

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…

math.AG2026

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…

math.AG2026

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…

math.AG2026

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…

math.AG2025

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{…