Infinitesimal Mixed Twistor Modules

Abstract

AbstractAny holonomic \(\mathcal{D}\)-module is locally expressed as the gluing of some meromorphic flat bundles on subvarieties. In this sense, meromorphic flat bundles are building blocks of holonomic \(\mathcal{D}\)-modules. In a similar sense, admissible variations of mixed twistor structure are building blocks of mixed twistor \(\mathcal{D}\)-modules. We shall study admissible variations of mixed twistor structure in Chap. 9 In this chapter, as a preliminary, we shall study the linear version of admissible variation of mixed Hodge structure, that is infinitesimal mixed twistor module. Infinitesimal mixed twistor structures naturally appear at the singularities of admissible variations of mixed twistor structure. Moreover, they contain much important information on the behaviour of the variations.KeywordsTensor ProductVector BundleComplex ManifoldFull SubcategoryInduce PolarizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.