School of Mathematics Colloquium

On Holomorphic Sectional Curvature and Fibration

by Dr. Ananya Chaturvedi (TIFR, Mumbai)

Thursday, November 22, 2018 from to (Asia/Kolkata)
at AG-69
Description
Abstract
A fibration, loosely speaking, is generalization of the concept of a fiber bundle. For a given fibration, we can talk about  its  two  “directions”:   base and fibers. Suppose  we  are  given  Hermitian  metrics  on  the  base and fibers of a holomorphic fibration such that the holomorphic sectional curvatures have same signs on the base and fibers.  Then, we show that the given metrics in the two “directions” can be used to construct a warped product metric on the total space such that this metric has the same sign of the holomorphic sectional curvature on the total space as that of the given metrics on the base and fibers.  The case of negative holomorphic sectional curvature was proved by Cheung in 1989.  In this talk, we shall focus on the positive holomorphic sectional curvature case.