Abstract
— Let X be a projective algebraic manifold of dimension n and let L be an ample line bundle over X . We give a numerical criterion ensuring that the adjoint bundle KX + L is very ample. The sufficient conditions are expressed in terms of lower bounds for the intersection numbers L ·Y over subvarieties Y of X . In the case of surfaces, our criterion gives universal bounds and is only slightly weaker than I. Reider’s criterion. When dimX ≥ 3 and codimY ≥ 2, the lower bounds for L · Y involve a numerical constant which depends on the geometry of X . By means of an iteration process, it is finally shown that 2KX +mL is very ample form ≥ 12n. Our approach is mostly analytic and based on a combination of Hormander’s L estimates for the operator ∂, Lelong number theory and the Aubin-Calabi-Yau theorem.
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