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

2014/07/28 by Ebenfelt, Peter
#32H02 #32Q10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.7476

Abstract

We consider local modifications ω_n+f^*ω_d of the Fubini-Study metric (with associated (1,1)-form ω_n) on an open subset Ω⊂ \bC\bPⁿ induced by a local holomorphic mapping f\colon Ω→ \bP^d. Our main result is that there are "gaps" in potential dimensions m such that the modification can be obtained as h^*ω_m for some local holomorphic mapping h\colon Ω→ \bC\bP^m. We also consider the case of rational conformal factors.

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