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arXiv · 1407.7476

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

Peter Ebenfelt
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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 $Ω\subset \bC\bP^n$ 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 $h^*ω_m$ for some local holomorphic mapping $h\colon Ω\to \bC\bP^m$. We also consider the case of rational conformal factors.

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Peter Ebenfelt. 2014-07-28. Local Holomorphic Isometries of a Modified Projective Space into a Standard Projective Space; Rational Conformal Factors. https://arxiv.org/abs/1407.7476

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