On the limit of spectral measures associated to a test configuration
arXiv:1211.2324
Abstract
We apply the integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt--Nyström so that the sequence of spectral measures for the induced -action on the central fiber converges to the canonical Duistermatt--Heckman measure defined by the associated weak geodesic ray. As a consequence, we show that the algebraic -norm of the test configuration equals to the -norm of tangent vectors. Using this result, We may give a natural energy theoretic explanation for the lower bound estimate on the Calabi functional by Donaldson and prove the analogous result for the Kähler--Einstein metric.
arXiv comment20 pages
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