2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60353We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective) flat connection on this family coming from a heat operator. They also possess modular properties similar to the classical ones.19 pages, 1 figure; Version for publicationAlgebraic Geometrytext