Admissible Mixed Twistor Structures and Their Variants

Abstract

In this chapter, we study admissible variations of mixed twistor structure and their variant. Let X be a complex manifold with a normal crossing hypersurface D. Let $\mathcal{V}$ be a smooth $\mathcal{R}_{X({\ast}D)}$-triple with a filtration W such that $(\mathcal{V},W)_{\vert X\setminus D}$ is a variation of mixed twistor structure. We are interested in the degeneration at any points of D. The relative monodromy filtration should control the weight filtration of the degenerated objects. If it is satisfied, $(\mathcal{V},W)$ is called an admissible variation of mixed twistor structure.