16,338 research outputs found
CM Stability of Projective varieties
We develop the connection between equivariant completions of algebraic
homogeneous spaces of reductive groups and lower bounds for the Mabuchi energy
of a polarized manifold over the space of Bergman metrics. We provide a new
definition of Tian's CM Polarization and discuss its properties.Comment: 52 pages, 3 figure
Projective duality and K-energy asymptotics
Let X be a smooth, linearly normal n dimensional complex projective variety.
Assume that the projective dual of X has codimension one with defining
polynomial D(X). In this paper the log of the norm of
D(X) is expressed as the restriction to the Bergman metrics of an energy
functional on X. We show how, for smooth plane curves, this energy functional
reduces to the standard action functionals of Kahler geometry.Comment: 27 page
CM Stability And The Generalized Futaki Invariant II
The Mabuchi K-energy map is exhibited as a singular metric on the refined CM
polarization of any equivariant family .
Consequently we show that the generalized Futaki invariant is the leading term
in the asymptotics of the reduced K-energy of the generic fiber of the map .
Properness of the K-energy implies that the generalized Futaki invariant is
strictly negative.Comment: 15, fully rewritten, references adde
Asymptotic density and the Ershov hierarchy
We classify the asymptotic densities of the sets according to
their level in the Ershov hierarchy. In particular, it is shown that for , a real is the density of an -c.e.\ set if and only if
it is a difference of left- reals. Further, we show that the densities
of the -c.e.\ sets coincide with the densities of the
sets, and there are -c.e.\ sets whose density is not the density of an
-c.e. set for any .Comment: To appear in Mathematical Logic Quarterl
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