Polynomial symplectomorphisms | Zendy

Janeczko Stanisław | Zendy; Jelonek Zbigniew | Zendy

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Polynomial symplectomorphisms

Author(s) -

Janeczko Stanisław,

Jelonek Zbigniew

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdm112

Subject(s) - mathematics , automorphism , symplectic geometry , polynomial , pure mathematics , group (periodic table) , field (mathematics) , algebra over a field , combinatorics , mathematical analysis , chemistry , organic chemistry

Let be the field of real or complex numbers. Let ( X ≅ 2 n , ω) be a symplectic affine space. We study the group of polynomial symplectomorphisms of X . We show that for an arbitrary k ∈ ℕ the group of polynomial symplectomorphisms acts k ‐transitively on X . Moreover, if 2 ⩽ l ⩽ 2 n − 2 then elements of this group can be characterized by polynomial automorphisms which preserve the symplectic type of all algebraic l ‐dimensional subvarieties of X .

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