Finite generation of canonical ring by analytic method

By Y. Siu. 2008

49 citations recorded by the source corpus.

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/02a30c363377a41c7fee1c616123aa9af2a9ecd2

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In Applied Mathematics

1. Robert J. Berman
2. S. Boucksom
3. J. Demailly
4. Chi Li
5. Tam'as Darvas
6. Ahmed Zeriahi
7. Vincent Guedj
8. Y. Odaka

In Geometry and Topology

1. Robert J. Berman
2. S. Boucksom
3. Chi Li
4. J. Demailly
5. Ahmed Zeriahi
6. Vincent Guedj
7. Tam'as Darvas
8. Mattias Jonsson

Citations in the corpus

• A variational approach to complex Monge-Ampère equations (2009, methodology): “[Siu08] Y. T. SIU, Finite generation of canonical ring by analytic method, Sci. China Ser.”
• The GIT-stability of Polarised Varieties via discrepancy (2008, background): “efined as the projective variety Proj⊕m≥0H 0(X,ω⊗m X ), whose canonical divisor is ample. It exists since the canonical ring ⊕m≥0H 0(X,ω⊗m X ) is a finitely generated algebra over C, due to [BCHM09] or [Siu08]. We use its relative version for log resolution of the original variety Xto try to prove Con”
• Alternate Compactifications of Moduli Spaces of Curves (2010, background): “ dimensional geometry. Indeed, one of the foundational theorems of higher dimensional geometry is that the canonical ring of a smooth projective variety of general type is nitely generated ([BCHM06], [Siu08], [Laz09]). A major impetus for work on this theorem was the fact that nite generation of can”
• Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds (2009, methodology): “The advantage of the analytic proof of the finite generation of the canonical ring is that its use of dynamic multiplier ideal sheaves explains completely transparently why the infinite blow-up process terminates and why the argument works (see [Siu2008, Remark(1.3.1)] and [Siu2008a, (1.2)(H)]).”
• Extension theorems, non-vanishing and the existence of good minimal models (2010, background): “The rest of the proof is based of the following global version of the H. Skoda division theorem (cf. [Skoda72]), established in [Siu08].”