Analysis of Geometric Stability
Sean Timothy Paul, Gang Tian
TL;DR
This paper investigates the relationship between CM and Chow polarizations on the Hilbert scheme, providing a numerical criterion for CM stability and an explicit formula for the generalized Futaki invariant.
Contribution
It introduces a numerical criterion for CM stability based on the difference between CM and Chow polarizations and derives an explicit formula for the generalized Futaki invariant.
Findings
Established the difference between CM and Chow polarizations on the Hilbert scheme.
Provided a numerical criterion for CM stability analogous to Mumford's G.I.T.
Derived an explicit formula for the generalized Futaki invariant in terms of weights and multiplicities.
Abstract
We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula for the generalised futaki invariant interms of weights and multiplicities of the associated degeneration.
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Taxonomy
TopicsGeometry and complex manifolds · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory