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# Holomorphic 2-Forms and Vanishing Theorems for Gromov--Witten Invariants

On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov--Witten invariants of $X$. This extends the approach used by Parker and the author for K\"{a}hler surfaces to higher dimensions.