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Rigidity of monodromies for Appell's hypergeometric functions

Haraoka Y., Kikukawa T.

Opuscula Mathematica

2015

Vol. 35, no. 5

567--594

For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeonietric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.

Local signature of fibered complex surfaces via moduli and monodromy

Ashikaga T.

Demonstratio Mathematica

2010

Vol. 43, nr 2

263-276

The signature of fibered complex surfaces is sometimes localized at finite fiber germs. We analyze this phenomenon by using datum of local monodromy in the mapping class group and a certain rational divisor on the moduli space of stable curves.