, Volume 7, Issue 1, pp 149-159

On genericity for holomorphic curves in four-dimensional almost-complex manifolds

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We consider spaces of immersed (pseudo-)holomorphic curves in an almost complex manifold of dimension four. We assume that they are either closed or compact with boundary in a fixed totally real surface, so that the equation for these curves is elliptic and has a Fredholm index. We prove that this equation is regular if the Chern class is ≥ 1 (in the case with boundary, if the ambient Maslov number is ≥ 1). Then the spaces of holomorphic curves considered will be manifolds of dimension equal to the index.