A twistor approach to the Kontsevich complexes

Abstract

We study the V-filtration of the mixed twistor $$\mathcal {D}$$ -modules associated to algebraic meromorphic functions. We prove that their relative de Rham complexes are quasi-isomorphic to the family of Kontsevich complexes. It reveals a generalized Hodge theoretic meaning of Kontsevich complexes. On the basis of the quasi-isomorphism, we revisit the results on the Kontsevich complexes due to H. Esnault, M. Kontsevich, C. Sabbah, M. Saito and J.-D. Yu from a viewpoint of mixed twistor $$\mathcal {D}$$ -modules.