The probabilistic vs the quantization approach to Kahler-Einstein geometry

• In the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic manifold X-involving random point processes on X-a key role is played by the partition function. In this work a new quantitative bound on the partition function is obtained. It yields, in particular, a new direct analytic proof that X admits a Kahler-Einstein metrics if it is uniformly Gibbs stable. The proof makes contact with the quantization approach to Kahler-Einstein geometry.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

monge-ampere equations

k-stability

metrics

curvature

bundles

energy

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)