Multiplier ideal sheaves in complex and algebraic geometry

By Y. Siu. 2005

100 citations recorded by the source corpus.

The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed. Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e3084d21d73be731a25ac276c9878194ece86d53

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In Computational Theory and Mathematics

1. Philippe Eyssidieux
2. Qi’an Guan
3. Jacob Sturm
4. Duong H. Phong
5. Vincent Guedj
6. Xiangyu Zhou
7. Ahmed Zeriahi

In Geometry and Topology

1. Robert J. Berman
2. Tam'as Darvas
3. Duong H. Phong
4. Jacob Sturm
5. Ahmed Zeriahi
6. Vincent Guedj
7. B. Berndtsson
8. Philippe Eyssidieux

In Mathematical Physics

1. Duong H. Phong
2. Jacob Sturm
3. Robert J. Berman
4. Ahmed Zeriahi
5. Philippe Eyssidieux
6. Vincent Guedj
7. Qi’an Guan
8. Xiangyu Zhou

Citations in the corpus

• Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow (2006, unknown): “R IC C I FLO W 1 D.H.Phong ,Natasa Sesum ,and Jacob Sturm y A bstract M ultiplieridealsheavesareconstructed asobstructionsto theconvergenceofthe K ahler-Ricci ow on Fano m anifolds,following earlier constructions ofK ohn,Siu, and Nadel,and using therecentestim atesofK olodziejand Perelm an.”
• Bergman kernels and the pseudoeffectivity of relative canonical bundles (2007, unknown): “We refer to [32], [33] for the details concerning the”
• Singular Kähler-Einstein metrics (2006, background): “One may also try to construct these singular KE metrics unconditionnally in an approach to the finiteness of the canonical ring [Siu2].”
• A survey of test ideals (2011, unknown): “[Siu05] Y.-T. Siu: Multiplier ideal sheaves in complex and algebraic geometry, Sci. China Ser.”
• A proof of Demailly's strong openness conjecture (2015, unknown): “, see [25], [7], [30], [31]).”
• Effectiveness of Demailly’s strong openness conjecture and related problems (2014, background): “Recall that the multiplier ideal sheaf I(φ) is the sheaf of germs of holomorphic functions f such that |f |2e−φ is locally integrable (see [32], see also [40], [41], [7], etc.”
• Lectures on Stability and Constant Scalar Curvature (2008, background): “Their applications to complex geometry have been pioneered by Siu [123, 124].”