We generalize the Demailly approximation theorem from complex geometry to Arakelov geometry. As an application, letX/Qbe an integral projective variety andNbe an adelic line bundle onX. We prove thatess(N)≥0Npseudo-effective. This was proved in [1], assumingNrelatively semipositive. We show...
Mathematics - Complex VariablesMathematics - Algebraic GeometryIn this article, we establish a sharp effectiveness result of Demailly's strong openness conjecture. We also establish a sharp effectiveness result related to a conjecture posed by Demailly and Koll\\'ar....
Mathematics - Complex VariablesMathematics - Algebraic GeometryMathematics - Differential GeometryWe prove the classical Nakano vanishing theorem with H\"ormander $L^2$-estimates on a compact K\"ahler manifold using Siu's so called $\\partial\\dbar$-Bochner-Kodaira method, thereby avoiding the K...
Lawrence Ein, Robert Lazarsfeld, and Michael Nakamaye, Zero-estimates, intersection theory, and a theorem of Demailly, Higher-Dimensional Complex Varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 183-207.Zero estimates, intersection theory, and a theorem of Demailly - Ein, Lazarsfeld, ...