RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 Video Library Archive Most viewed videos Search RSS New in collection

You may need the following programs to see the files

International conference "Birational and affine geometry"
April 26, 2012 14:00–14:50, Moscow, Steklov Mathematical Institute of RAS

Fundamental group of some genus-$2$ fibrations and applications

R. V. Gurjar

Tata Institute of Fundamental Research, Mumbai
 Video records: Flash Video 331.0 Mb Flash Video 2,012.4 Mb MP4 331.0 Mb

Abstract: We will prove that given a genus-$2$ fibration $f\colon X \to C$ on a smooth projective surface $X$ such that $b_1(X)=b_1(C)+2$, the fundamental group of $X$ is almost isomorphic to $\pi_1(C) \times \pi_1(E)$, where $E$ is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces $X$ with genus-$2$ fibration $X\to C$ such that $b_1(X)>b_1(C)$. This is joint work with Sagar Kolte.