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Let $V^L$ and $V^R$ be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let $F$ be a conformal full field algebra over $V^L\otimes V^R$. We prove that the $q_{\tau }$-$\overline{q_{\tau }}$-traces (natural traces involving $q_{\tau }=e^{2\pi i\tau }$ and $\overline{q_{\tau }}=\overline{e^{2\pi i\tau }}$) of geometrically modified genus-zero correlation functions for $F$ are convergent in suitable regions and can be extended to doubly periodic functions with periods $1$ and $\tau$.

We obtain necessary and sufficient conditions for these functions to be modular invariant. In the case that $V^L=V^R$ and $F$ is one of those constructed by the authors in (Y.-Z. Huang and L. Kong, Full field algebras, to appear; math.QA/0511328), we prove that all these functions are modular invariant.