Seminars

 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 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.