A principle governing deformation theory with cohomology constraints in characteristic zero, generalizing Deligne's deformation theory principle, was developed together with B. Wang, M. Rubio in terms of dg Lie modules, and, more generally, $\text{L}\infty$ modules. An application of this theory is that for a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first non-zero Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit.[-]