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Bulletin of the London Mathematical Society Advance Access originally published online on February 5, 2008
Bulletin of the London Mathematical Society 2008 40(1):108-116; doi:10.1112/blms/bdm112
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© 2008 London Mathematical Society

Polynomial symplectomorphisms

Stanislaw Janeczko

Instytut Matematyczny PAN
ul. Sniadeckich 8
00-956 Warszawa
Poland
Wydzial Matematyki i Nauk
Informacyjnych PW
Pl. Politechniki 1
00-661 Warszawa
Poland

Zbigniew Jelonek

Instytut Matematyczny PAN
Sw. Tomasza 30
31-027 Kraków
Instytut Matematki
Akademia Swietokrzyska
Kielce, Poland
najelone@cyf-kr.edu.pl

Received 23 May 2006.

Let K be the field of real or complex numbers. Let (X {cong} K2n, {omega}) be a symplectic affine space. We study the group of polynomial symplectomorphisms of X. We show that for an arbitrary k isin N the group of polynomial symplectomorphisms acts k-transitively on X. Moreover, if 2 ≤ l ≤ 2n – 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.

2000 Mathematics Subject Classification 51N10, 51N20, 15A04.

The second author was partially supported by the grant ofPolish Ministry of Science, 2006–2009.


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