On first order elliptic equations for sections of complex line bundles

We construct closed complex submanifolds of $ℂ^{n}$ which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of $ℂ^{n}$ .

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

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In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

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