2005/10/21 by Mikhail Kapranov, Kapranov, M., Éric Vasserot +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.math/0510476
openalex publication_date 2005/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To any algebraic variety X and and closed 2-form ωon X, we associate the "symplectic action functional" T(ω) which is a function on the formal loop space LX introduced by the authors in math.AG/0107143. The correspondence ω--> T(ω) can be seen as a version of the Radon transform. We give a characterization of the functions of the form T(ω) in terms of factorizability (infinitesimal analog of additivity in holomorphic pairs of pants) as well as in terms of vertex operator algebras. These results will be used in the subsequent paper which will relate the gerbe of chiral differential operators on X (whose lien is the sheaf of closed 2-forms) and the determinantal gerbe of the tangent bundle of LX (whose lien is the sheaf of invertible functions on LX). On the level of liens this relation associates to a closed 2-form ωthe invertible function exp T(ω).