Complex subtorus

A complex subtorus of $V/\Gamma$ is a connected closed complex Lie subgroup. It has the form $V^{\prime }/{\Gamma }^{\prime }$ for a complex subspace $V^{\prime }\subseteq V$ such that ${\Gamma }^{\prime }=V^{\prime }\cap \Gamma$ is a full lattice in $V^{\prime }$.