Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds

By Y. Siu. 2009

48 citations recorded by the source corpus.

This note is written for the Festschrift in honor of Professor Christer Kiselman. Multiplier ideal sheaves identify the location and the extent of the failure of crucial estimates. In this note we will discuss and explain the historic evolution of the notion of multiplier ideal sheaves, especially the interpretation from the viewpoint of destabilizing subsheaves in the context of terminating or bounding an infinite process. We will also discuss the approach of constructing rational curves in Fano manifolds by using dynamic multiplier ideal sheaves and singularity-magnifying complex Monge-Ampere equations. This approach is still under development with details in the process of being worked out. We will indicate where details still need to be worked out.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/40168206b8377c6515f88d0f49d8a147bcfdb513

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In Geometry and Topology

1. Qi’an Guan
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Citations in the corpus

• A survey of test ideals (2011, unknown): “We invite the reader to see [Laz04, Ein97, ELSV04, Siu05, Siu09] for more background.”
• 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 [33], see also [7,27,29,32,41,42], etc.”