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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 .