Harmonic total Chern forms and stability

Details Harmonic total Chern forms and stability Harmonic total Chern forms and stability

2006-03-30

arxiv.org/abs/math/0603706v2

Mathematics

Differential Geometry

20 pages, to appear in Kodai Mathematical Journal

Scientific paper

In this paper we will perturb the scalar curvature of compact Kahler manifolds by incorporating it with higher Chern forms, and then show that the perturbed scalar curvature has many common properties with the unperturbed scalar curvature. In particular the perturbed scalar curvature becomes a moment map, with respect to a perturbed symplectic structure, on the space of all complex structures on a fixed symplectic manifold, which extends the results of Donaldson and Fujiki on the unperturbed case.

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