Orthogonal projection of a test configuration to vector fields

Abstract

Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associated ${\mathbb{C}}^{\ast }$-actions. We show that there actually holds the moment convergence of the weight distributions. Our analytic approach at the same time specifies the limit in terms of the weak geodesic ray associated with the test configuration. Related to the result, we discuss about the reduced $L^p$-norm of the test configuration in attempt to describe the uniform K-stability of the polarization relative to the automorphism group.

arXiv comment17 pages, The main point of the paper is rearranged. Accordingly, abstract and introduction are fixed

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Cited by in corpus (3)

• Stability and coercivity for toric polarizations
• The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
• Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons