Video library: R. V. Gurjar, Fundamental group of some genus-$2$ fibrations and applications

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

Fundamental group of some genus-$2$ fibrations and applications R. V. Gurjar Tata Institute of Fundamental Research, Mumbai
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. Language: English