Stability and Futaki Invariants of Fano Hypersurfaces

Details Stability and Futaki Invariants of Fano Hypersurfaces Stability and Futaki Invariants of Fano Hypersurfaces

2001-11-09

arxiv.org/abs/math/0111116v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability of X w.r.t. a certain polarization. He conjectures that each of these conditions is also sufficient for the existence of such a metric. If this is true, then in particular the two stability conditions would be equivalent. We show that for Fano hypersurfaces in projective space, where due to the work of Lu and Yotov an explicit formula for the Futaki invariant is known, these two conditions are indeed very closely related.

Affiliated with

Also associated with

No associations

Rating

Stability and Futaki Invariants of Fano Hypersurfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability and Futaki Invariants of Fano Hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability and Futaki Invariants of Fano Hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539625