11,476 research outputs found

### Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces

We prove that a germ of a holomorphic map $f$ between $C^n$ and $C^{n'}$
sending one real-algebraic submanifold $M\subset C^n$ into another $M'\subset
C^{n'}$ is algebraic provided $M'$ contains no complex-analytic discs and $M$
is generic and minimal. We also propose an algorithm for finding
complex-analytic discs in a real submanifold.Comment: 12 pages An algorithm for finding complex-analytic discs in a real
submanifold is adde

### Germs of local automorphisms of real-analytic CR structures and analytic dependence on $k$-jets

The topic of the paper is the study of germs of local holomorphisms $f$
between $C^n$ and $C^{n'}$ such that $f(M)\subset M'$ and $df(T^cM)=T^cM'$ for
$M\subset C^n$ and $M'\subset C^{n'}$ generic real-analytic CR submanifolds of
arbitrary codimensions. It is proved that for $M$ minimal and $M'$ finitely
nondegenerate, such germs depend analytically on their jets. As a corollary, an
analytic structure on the set of all germs of this type is obtained.Comment: 17 page

### On the automorphism groups of algebraic bounded domains

Let $D$ be a bounded domain in $C^n$. By the theorem of H.~Cartan, the group
$Aut(D)$ of all biholomorphic automorphisms of $D$ has a unique structure of a
real Lie group such that the action $Aut(D)\times D\to D$ is real analytic.
This structure is defined by the embedding $C_v\colon Aut(D)\hookrightarrow
D\times Gl_n(C)$, $f\mapsto (f(v), f_{*v})$, where $v\in D$ is arbitrary. Here
we restrict our attention to the class of domains $D$ defined by finitely many
polynomial inequalities. The appropriate category for studying automorphism of
such domains is the Nash category. Therefore we consider the subgroup
$Aut_a(D)\subset Aut(D)$ of all algebraic biholomorphic automorphisms which in
many cases coincides with $Aut(D)$. Assume that $n>1$ and $D$ has a boundary
point where the Levi form is non-degenerate. Our main result is theat the group
$Aut_a(D)$ carries a unique structure of an affine Nash group such that the
action $Aut_a(D)\times D\to D$ is Nash. This structure is defined by the
embedding $C_v\colon Aut_a(D)\hookrightarrow D\times Gl_n(C)$ and is
independent of the choice of $v\in D$.Comment: 29 pages, LaTeX, Mathematischen Annalen, to appea

### Semiclassical spin coherent state method in the weak spin-orbit coupling limit

We apply the semiclassical spin coherent state method for the density of
states by Pletyukhov et al. (2002) in the weak spin-orbit coupling limit and
recover the modulation factor in the semiclassical trace formula found by Bolte
and Keppeler (1998, 1999).Comment: 12 pages including 1 encapsulated figur

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