, Volume 50, Issue 4, pp 647-657

Theta functions on T 2-bundles over T 2 with the zero Euler class

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Abstract

We construct an analog of the classical theta function on an abelian variety for the closed 4-dimensional symplectic manifolds that are T 2-bundles over T 2 with the zero Euler class. We use our theta functions for a canonical symplectic embedding of these manifolds into complex projective spaces (an analog of the Lefschetz theorem).

Original Russian Text Copyright © 2009 Egorov D. V.
The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00598-a).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 4, pp. 818–830, July–August, 2009.