Local Holomorphic Isometries of a Modified Projective Space into a Standard Projective Space; Rational Conformal Factors

Abstract

We consider local modifications ${\omega }_n+f^{\ast }{\omega }_d$ of the Fubini-Study metric (with associated $(1,1)$-form ${\omega }_n$) on an open subset $Ω\subset \bC\bP^n$ induced by a local holomorphic mapping $f\colon Ω\to \bP^d$. Our main result is that there are "gaps" in potential dimensions $m$ such that the modification can be obtained as $h^{\ast }{\omega }_m$ for some local holomorphic mapping $h\colon Ω\to \bC\bP^m$. We also consider the case of rational conformal factors.

References in corpus (1)

• An Application of Macaulay's Estimate to CR Geometry