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).
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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.
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Egorov, D.V. Theta functions on T 2-bundles over T 2 with the zero Euler class. Sib Math J 50, 647–657 (2009). https://doi.org/10.1007/s11202-009-0072-x
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DOI: https://doi.org/10.1007/s11202-009-0072-x