2000/11/16 by Ilia Zharkov, Zharkov, Ilia
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0011112
19 pages, 1 figure; Version for publication
arxiv created 2003/07/10 · arxiv updated 2009/11/30
We 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.