Integral Hermitian forms on the square complex torus (source code)

= Integral Hermitian forms on the square complex torus
{title2=$H_t(z,w)=t z\overline w,\quad t\in\mathbb Z$}

On $\mathbb C/(\mathbb Z+\mathbb Zi)$, a <Hermitian form> linear in its first argument has integral imaginary part on the <period lattice> exactly when its real scalar coefficient is integral. Positivity is equivalent to $t>0$. The associated <holomorphic line bundle> has degree $t$ because its <First Chern class> is represented by $(it/2)dz\wedge d\overline z$. In particular the oriented Chern pairing is minus the imaginary part under this convention.