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

Published:2009-03-01
Printed: Mar 2009
• Junho Lee
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## Abstract

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.
 MSC Classifications: 53D45 - Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]