Fields of CR meromorphic functions
| dc.creator | Hill, C. Denson | |
| dc.creator | Nacinovich, Mauro | |
| dc.date | 2007-10-26 | |
| dc.date.accessioned | 2026-07-07T08:38:53Z | |
| dc.date.available | 2026-07-07T08:38:53Z | |
| dc.description | Let $M$ be a smooth compact $CR$ manifold of $CR$ dimension $n$ and $CR$ codimension $k$, which has a certain local extension property $E$. In particular, if $M$ is pseudoconcave, it has property $E$. Then the field $\Cal K(M)$ of $CR$ meromorphic functions on $M$ has transcendence degree $d$, with $d\leq n+k$. If $f_1, f_2, \hdots , f_d$ is a maximal set of algebraically independent $CR$ meromorphic functions on $M$, then $\Cal K(M)$ is a simple finite algebraic extension of the field $\Bbb C(f_1, f_2, \hdots, f_d)$ of rational functions of the $f_1, f_2, \hdots , f_d$. When $M$ has a projective embedding, there is an analogue of Chow's theorem, and $\Cal K(M)$ is isomorphic to the field $\Cal R(Y)$ of rational functions on an irreducible projective algebraic variety $Y$, and $M$ has a $CR$ embedding in $\roman{reg} Y$. The equivalence between algebraic dependence and analytic dependence fails when condition $E$ is dropped. | |
| dc.identifier | https://arxiv.org/abs/0710.5166 | |
| dc.identifier | http://arxiv.org/abs/0710.5166 | |
| dc.identifier | Rend. Sem. Mat. Univ. Padova 111 (2004), 179-204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140894 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Fields of CR meromorphic functions | |
| dc.type | text |