Multiplier ideal sheaves and analytic methods in algebraic geometry

By J. Demailly. 2000

199 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/591003dfa77955ae1758cec4a95a27dc9969b4d8

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1. Chi Li
2. Robert J. Berman
3. Mattias Jonsson
4. S. Boucksom
5. C. Favre
6. Qi’an Guan
7. Junyan Cao
8. B. Berndtsson

Citations in the corpus

• Valuations and multiplier ideals (2004, background): “C has diameter 1. It is given by dC(C, D) = m(C)m(D)/C � D . (See [FJ1, Lemma 3.56].)”
• Toric plurisubharmonic functions and analytic adjoint ideal sheaves (2010, methodology): “The approach we used to show this result, which relies in an essential manner on the local version of Manivel’s theorem, is a natural way to obtain the global version of Manivel’s theorem [5].”
• On a non-vanishing conjecture of Kawamata and the core of an ideal (2003, background): “In recent years, multiplier ideals have found many rich applications to algebraic geometry, particularly to issues of effectiveness; see [8], [42].”
• Frankel conjecture and Sasaki geometry (2012, background): “By an algebraic manipulation (see [20] Proposition 10.”
• The openness conjecture and complex Brunn-Minkowski inequalities (2014, background): “Let us first state the ‘strong openness conjecture’ from Demailly [9].”
• Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications (2014, result): “ fundamental importance in algebraic and analytic geometry. After the crucial contribution of [OT87], [Ohs88], this result has been generalized by many authors in various contexts, including [Man93], [Dem01], [Ber05], [Che11], [Li12], [ZGZ12], [Blo 13], [GZ13a]. In this article we treat yet another ”
• A TRANSCENDENTAL APPROACH TO KOLL AR'S INJECTIVITY THEOREM II (2007, methodology): “A weakly 1-complete manifold X is called a weakly pseudoconvex manifold in [4].”
• A proof of Demailly's strong openness conjecture (2015, background): “In the present article, we discuss a more general conjecture — the strong openness conjecture about multiplier ideal sheaves for plurisubharmonic functions, which was posed by Demailly in [7] and [8] (see also [11]):”
• Jumping coefficients of multiplier ideals (2003, background): “By considering the neighboring pairs of ideals in the chain OX ⊇ J ( aξ1 ) ⊇ J ( aξ2 ) ⊇ . . . ⊇ J ( aξℓ ) , one then arrives at an effective uniform Artin-Rees number for any of the multiplier ideals J ( ac ) : Corollary 3.2.”