Research Seminar 4
Date/Time: 15.09.2021, 2:15 pm.
PICARD GROUPS OF CERTAIN COMPACT COMPLEX PARALLELIZABLE MANIFOLDS AND RELATED SPACES
Pritthijit Biswas
Chennai Mathematical Institute.
15-09-21

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Abstract

Let $G$ be a complex simply connected semisimple Lie group and let $\Gamma$ be a torsionless irreducible and uniform lattice. Then $G/\Gamma$ is a compact complex non-Kähler manifold whose tangent bundle is holomorphically trivial. We compute the Picard group of $G/\Gamma$. When $rank(G)\ge 2,$ we also show that $Pic^0(P_{\Gamma})\cong Pic^0(Y)$ where $P_{\Gamma}$ is a $G/\Gamma$ bundle associated to a holomorphic principle $G$ bundle over a compact connected complex manifold $Y,$ and, when $rank(G)\ge 3,$ we show that $Pic(Y)\longrightarrow Pic(P_{\Gamma})$ is injective with finite cokernel.

This is a joint work with Parameswaran Sankaran.