Claire Voisin

Claire Voisin is a French mathematician whose work in algebraic geometry and Hodge theory includes major contributions to complex projective varieties and algebraic cycles.

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Algebraic geometry: The study of geometric objects defined by polynomial equations and the maps between them. This is the broad mathematical field in which Voisin made her career.
Jean-Pierre Serre: A French mathematician whose work shaped algebraic topology, algebraic geometry, and number theory. Serre’s influence on modern algebraic geometry forms part of the mathematical tradition surrounding Voisin’s work.
Hodge conjecture: A conjecture that rational Hodge classes on a smooth complex projective variety are classes of algebraic cycles. Voisin’s work investigates the conjecture and the limits of its algebraic-cycle predictions.
Griffiths group: The group of homologically trivial algebraic cycles modulo algebraic equivalence. Voisin’s constructions reveal how large and subtle these groups can be.
Theorem of Voisin: A name used for several distinct results by Claire Voisin in algebraic geometry. Her name is attached to multiple theorems, so this link distinguishes the eponymous results.
Hodge theory: A framework relating the topology of complex algebraic varieties to their differential forms and algebraic structure. Voisin’s work develops Hodge-theoretic methods for studying algebraic varieties.
Maxim Kontsevich: A Russian-French mathematician known for contributions to geometry, topology, and mathematical physics. Kontsevich shared the 2008 Crafoord Prize with Voisin for advances in algebraic geometry.
Integral Hodge conjecture: The integral version of the Hodge conjecture, asserting that integral Hodge classes are algebraic cycle classes. Voisin constructed examples showing that this stronger formulation can fail.
Rationality problem: The problem of determining whether an algebraic variety is birationally equivalent to projective space. Her work supplies powerful obstructions to stable rationality in this area.
Lefschetz conjecture on (1,1) classes: The theorem that integral cohomology classes of type (1,1) on a smooth projective variety are divisor classes. This foundational result provides a solved low-codimension model for the Hodge conjecture.