Abstract
This chapter discusses the definition of admissible variations of mixed Hodge structure (VMHS), the results of M. Kashiwara in A study of variation of mixed Hodge structure (1986), and applications to the proof of algebraicity of the locus of certain Hodge cycles. It begins by recalling the relations between local systems and linear differential equations as well as the Thom–Whitney results on the topological properties of morphisms of algebraic varieties. The definition of a VMHS on a smooth variety is given, and the singularities of local systems are discussed. The chapter then studies the properties of degenerating geometric VMHS. Next it gives the definition and properties of admissible VMHS and reviews important local results of Kashiwara. Finally, the chapter recalls the definition of normal functions and explains recent results on the algebraicity of the zero set of normal functions.
Published Version
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