Analytic Methods in Algebraic Geometry

By J. Demailly. 2007

467 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d346bf6ce7d1be4d0bdabf068c5bcb3198958783

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A sharp effectiveness result of Demailly's strong openness conjecture (2017, background): “ and Kollar. 1. Introduction The multiplier ideal sheaf related to a plurisubharmonic function plays an important role in complex geometry and algebraic geometry, which was widely discussed (see e.g. [34, 24, 29, 6, 7, 3, 8, 22, 31, 32, 4]). We recall the deﬁnition as follows. Let ϕbe a plurisubharm”
A proof of Demailly's strong openness conjecture (2015, background): “20) in [8]; see also [22]), one can obtain the following lemma: Lemma 2.”
A solution of an L 2 extension problem with an optimal estimate and applications (2015, background): “[14] J.-P. Demailly, Estimations L2 pour l’opérateur ∂̄ d’un fibré vectoriel holomor- phe semi-positif au-dessus d’une variété kählérienne complète, Ann.”
Optimal constant in an L2 extension problem and a proof of a conjecture of Ohsawa (2014, unknown): “ is the space of smooth diﬀerential (n,q)-forms with values in Ewith compact support, we have k(η+g−1)12 D′′∗αk2 +kη 1 2 D′′αk2 >hh[η √ −1ΘE− √ −1∂∂η¯ − √ −1g∂η∧∂η,¯ Λω]α,αii. (2.2) Lemma 2.4 (See [11,14]). Let X be a complete K¨ahler manifold equipped with a (not necessarily complete) K¨ahler me”
Effectiveness of Demailly’s strong openness conjecture and related problems (2014, background): “In [20,21], the authors solved the strong openness conjecture posed by Demailly in [6,7] (see also [3,4,9,11,23,25,26,30,31,45], etc.”
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (2013, methodology): “bdd(F,h) := sup{k∈ Z| limsup m→∞ dimH0 bdd,hm(X,F m) mk >0}. If hmin is a metric with minimal singularities on F, the norm |s|hm min is bounded on X for any section s∈ H0(X,Fm). (For example see [Dem] or [Mat15b].) It implies that H0 bdd,hm min (X,Fm) is isomorphic to H0(X,Fm) for every m≥ 0. In”
A general extension theorem for cohomology classes on non reduced analytic subspaces (2017, background): “ some local coordinates near x0. As usual, we also denote by KX = ΛnT∗ X the canonical bundle of an n-dimensional complex manifold X. As is well known, I(e−ϕ) ⊂ OX is a coherent ideal sheaf (see e.g. [Dem-book]). Our main result is given by the following general statement. Date: April 4, 2017, versi”
Albanese maps of projective manifolds with nef anticanonical bundles (2016, background): “r to [BP08, BP10, Fuj16, Hor10, Kaw82, Kaw98, Kol85, PT14, Tsu10, Vie83, Vie95] to quote only a few. To be begin with, we ﬁrst recall the deﬁnition of possibly singular hermitian metrics. We refer to [Dem12] for more details. Let X be a projective manifold and let L → X be a line bundle on X endowed”
Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, unknown): “hat |∇χR| <C′/R, for a constant C′ independent of R. We can regard the (0,1)-form χRv (1) i as a (n,1)-form valued in the anti-canonical line bundle. From the Bochner-Kodaira formula (see (4.7) of [8]), we have (3.14) ˆ B(pi,R) ( √ −1∂ j∂¯kϕi+Ric g i jk )(χRv (1) i )¯(χRv (1) i )¯ke −ϕ ≤ k∂¯(χRv ”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, background): “[15] J.-P. Demailly, Estimations L2 pour l’opérateur d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète.”