A uniqueness theorem for automorphisms of a nondegenerate surface in a complex space

Beloshapka, V. K.

doi:10.1007/bf01138501

Cited by 31 publications

(34 citation statements)

References 2 publications

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“…On the other hand, for all tensors a, r which satisfy system (7), (8) It corresponds to a 1-parameter subgroup {(I)t} of automorphisms of Q that coincides with the initial automorphism for t = 1. This reasoning establishes a 1-to-1 correspondence between Aut0,id and .,4 x ~, where .A is the complex linear space of all a satisfying (7), and T~ is the N-linear space of all r satisfying (8).…”

Section: G O R = R~e ~ (25)mentioning

confidence: 95%

“…(7), (8). On the other hand, for all tensors a, r which satisfy system (7), (8) It corresponds to a 1-parameter subgroup {(I)t} of automorphisms of Q that coincides with the initial automorphism for t = 1.…”

Section: G O R = R~e ~ (25)mentioning

confidence: 96%

“…After a suitable linear coordinate change in w-variables the equation of Q takes the form Imw I = 0. We use the notation Auto M for the group of local isotropic automorphisms of M, i.e., of germs of biholomorphic maps ~ defined in a neighborhood of the origin such that ~(0) = 0, and ~(M) C M. In 1990, Belo~apka [8] proved the following theorem:…”

Section: Description Of the Infinitesimal Automorphismsmentioning

confidence: 99%

See 2 more Smart Citations

Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains

Ežov¹,

Schmalz²

1998

J Math Sci

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Section: G O R = R~e ~ (25)mentioning

confidence: 95%

Section: G O R = R~e ~ (25)mentioning

confidence: 96%

Section: Description Of the Infinitesimal Automorphismsmentioning

confidence: 99%

See 1 more Smart Citation

Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains

Ežov¹,

Schmalz²

1998

J Math Sci

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“…Consider all holomorphic vector fields on Q such that their restriction to Q is tangent to Q (Q is a nondegenerate (k, n)-quadric). In [3] Beloshapka proved that all such fields have the specific form a s…”

Section: (Cz + Aw + A(z Z) + B(z W)) :--Z + (Sw + 2i{z A~) + R(w mentioning

confidence: 98%

About C-rigid quadrics

Palinchak

1996

Math Notes

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ABSTRACT. In the article strongly nondegenerate (h, n)-quadrics all of whose linear automorphisms are of the form z ~ pz, to ~ I/~12,~, p E C \ {0} are considered. Quadrics all of whose linear automorphisms are of this form were called c-rigid by V. Beloshapka. The main result of the article is the following: any c-rigid strongly nondegenerate (h, n)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for (h, n)-quedrics is presented.

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“…Statement [2][3][4]. For the group Aut(M) of transformations of C "+k biholomorphie in a neighborhood of the origin and mapping the germ of M at the origin into itself, we have …”

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confidence: 99%

Invariants of CR-manifolds associated with the tangent quadric

Beloshapka

1996

Math Notes

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ABSTRACT. We construct a system of CR-invariants of a manifold generated by projective invariants of the tangent quadric. We present a description of the group of projective diffeomorphisrns of a quartic. We also estimate the degree of a rational mapping of a quartic. The description problem for subgroups of a Cremona group of bounded degree is posed.w Introduction Consider the germ M of a smooth real surface at the origin of the complex linear space of dimension N _> 2. Then in some neighborhood of the origin the germ M may be given by the system of equationsIf the vectors {grad~a(0), p = 1,..., k} are C-linearly independent, a complex linear transformation takes the equations of M to the formhere F is a smooth mapping of a neighborhood of the origin in C n x R k into R k , and F and dF vanish at Z = 0, ReW = 0. Among such manifolds one meets (k, n)-quadrics, i.e., surfaces of the formwhere ( i.e., the surface and the quadric are tangent up to the third order. In this case the (k, n)-quadric, which we denote by Q, is called the tangent quadric to the surface M. Note that the dimension of M is k + 2n, Im W = 0 is the equation of the tangent plane at the origin, W = 0 is the equation of the complex tangent plane, i.e., n is the dimension of the complex tangent plane; and (Z, Z) is the Levi form of the surface M at the origin. Let us recall some information on tangent quartics.

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A uniqueness theorem for automorphisms of a nondegenerate surface in a complex space

Cited by 31 publications

References 2 publications

Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains

Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains

About C-rigid quadrics

Invariants of CR-manifolds associated with the tangent quadric

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