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Theta-functions for indefinite polarizations

Ilia Zharkov
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Abstract

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.

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Ilia Zharkov. 2003-07-10. Theta-functions for indefinite polarizations. https://arxiv.org/abs/math/0011112

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