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- W1507381270 abstract "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 $dleq n+k$. 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." @default.
- W1507381270 created "2016-06-24" @default.
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- W1507381270 date "2007-10-26" @default.
- W1507381270 modified "2023-09-27" @default.
- W1507381270 title "Fields of CR meromorphic functions" @default.
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