Strictly regular and cscK metrics

Abstract

A Kaehler metric $g$ with integral Kaehler form is said to be partially regular if the partial Bergman kernel associated to mg is a positive constant for all integer m sufficiently large. The aim of this paper is to prove that for all n\geq 2 there exists an n-complex dimensional manifold equipped with strictly partially regular and cscK metric g. Further, for n\geq 3, the (constant) scalar curvature of g can be chosen to be zero, positive or negative.

arXiv comment8 pages, to appear in International Journal of Mathematics

References in corpus (6)

• Kaehler-Einstein submanifolds of the infinite dimensional projective space
• On the third coefficient of TYZ expansion for radial scalar flat metrics
• Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kaehler manifolds
• Finite TYCZ expansions and cscK metrics
• Interface asymptotics of Partial Bergman kernels around a critical level
• Pointwise Weyl laws for Partial Bergman kernels