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Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.

Let L be an ample line bundle on a Kähler manifolds of nonpositive sectional curvature with K as the canonical line bundle. We give an estimate of m such that K+mL is very ample in terms of the injectivity radius. This implies that m can be chosen arbitrarily small once we go deep enough into a tower of covering of the manifold. The same argument gives an effective Kodaira Embedding Theorem for compact Kähler manifolds in terms of sectional curvature and the injectivity radius. In case of locally Hermitian symmetric space of noncompact type or if the sectional curvature is strictly negative, we prove that K itself is very ample on a large covering of the manifold.

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Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces

Very Ampleness of Line Bundles and Canonical Embedding of Coverings of Manifolds

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Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces

Very Ampleness of Line Bundles and Canonical Embedding of Coverings of Manifolds