# Count of Genus Zero J-Holomorphic Curves in Dimensions Four and Six

Ahmet Beyaz

Arxiv ID: 0906.5472•Last updated: 11/11/2021

In this note, genus zero Gromov-Witten invariants are reviewed and then
applied in some examples of dimension four and six. It is also proved that the
use of genus zero Gromov-Witten invariants in the class of embedded
$J$-holomorphic curves to distinguish the deformation types of symplectic
structures on a smooth $6$-manifold is restricted in the sense that they can
not distinguish the symplectic structures on $X_1\times S^2$ and $X_2\times
S^2$ for two minimal, simply connected, symplectic $4$-manifolds $X_1$ and
$X_2$ with $b_2^+(X_1)>1$ and $b_2^+(X_2)>1$.

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