Characterizing quasi-isometric rigidities for holomorphic fibrations by monodromy

Speaker: Yibo Zhang (Institut Fourier at Grenoble)

Time: 5/16, Friday, 2-3:30 pm
Location: Simis 1510

Abstract: A holomorphic fibration is a complex 2-dimensional manifold endowed with a holomorphic projection onto a hyperbolic Riemann surface, where the generic fiber is a closed Riemann surface, though a finite number of fibers may have singularities. The monodromy of such a fibration encodes its topological structure and its analytic structure can be investigated through the classifying map: a holomorphic map from the hyperbolic base surface to the moduli space of closed Riemann surfaces. The image of this map is called a holomorphic curve in the moduli space.
In this talk, we explore the shape of a holomorphic curve and show that, when all peripheral monodromies are of infinite order, the holomorphic curve is quasi-isometrically immersed with respect to the intrinsic Kobayashi distance. We also show that the quasi-isometric rigidity for the lift of a holomorphic curve is fully characterized by its monodromy.