On the Picard number and the extension degree of period matrices of complex tori

Robert Auffarth, Jorge Duque Franco

The rank $\ddot{I}$ of the Néron-Severi group of a complex torus $X$ of dimension $g$ satisfies $0\le \ddot{I}\le g^2=h^{1,1}.$ The degree $\mathfrak{d}$ of the extension field generated ove…