Multiplier ideal sheaves and geometric problems
Akito Futaki, Yuji Sano
TL;DR
This paper reviews the role of multiplier ideal sheaves in solving geometric problems in Kählerian and Sasakian geometries, highlighting recent results on obstructions to Kähler-Einstein metrics on Fano manifolds.
Contribution
It provides an overview of multiplier ideal sheaves and presents new findings on their support and relation to obstructions in Kähler-Einstein metric existence.
Findings
Support of subschemes relates to obstructions of Kähler-Einstein metrics.
Recent results connect multiplier ideal sheaves to geometric invariants.
Obstructions are characterized by non-vanishing invariants.
Abstract
In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in K\"ahlerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut out by multiplier ideal sheaves and the invariant whose non-vanishing obstructs the existence of K\"ahler-Einstein metrics on Fano manifolds.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory