11,476 research outputs found

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

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    We prove that a germ of a holomorphic map ff between CnC^n and Cnβ€²C^{n'} sending one real-algebraic submanifold MβŠ‚CnM\subset C^n into another Mβ€²βŠ‚Cnβ€²M'\subset C^{n'} is algebraic provided Mβ€²M' contains no complex-analytic discs and MM 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 kk-jets

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    The topic of the paper is the study of germs of local holomorphisms ff between CnC^n and Cnβ€²C^{n'} such that f(M)βŠ‚Mβ€²f(M)\subset M' and df(TcM)=TcMβ€²df(T^cM)=T^cM' for MβŠ‚CnM\subset C^n and Mβ€²βŠ‚Cnβ€²M'\subset C^{n'} generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for MM minimal and Mβ€²M' 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

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

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

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    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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