The set of fixed points of an algebraic group

• Autorzy: Jelonek Z.
• Języki publikacji: EN

Abstrakty

EN

Let G be an algebraic group, which acts effectively on an affine space C[sup n]. Assume that a hypersurface W [is a subset of a set] C[sup n] is contained in the set of fixed point of G. Then W is a C-uniruled variety, i.e. there exists a n - 1-dimensional affine cylinder R x C and a dominant, generically-finite polynomial mapping phi : R x C --> W.

Słowa kluczowe

EN

affine space; algebraic group; set of fixed points

PL

przestrzeń afiniczna; grupa algebraiczna; zbiór punktów stałych

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 1
• Strony: 69--73
• Opis fizyczny: Bibliogr 6 poz.

Twórcy

autor

Jelonek Z.

• Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland,

Bibliografia

• [1] A. Białynicki-Birula, Some theorems on actions of algebraic groups Annals of Math., 98 (1973) 480-497.
• [2] S. Iitaka, Algebraic geometry, Springer-Verlag, New York 1982.
• [3] Z. Jelonek, The automorphisms group of Zariski open affine subset of th plane, Ann. Polon. Math., 62 (1994) 163-171.
• [4] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z., 212 (1993) 113-120.
• [5] Z. Jelonek, Affine smooth varieties with finite group of automorphisms, Math. Z., 216 (1994) 575-591.
• [6] Z. Jelonek, Testing sets for properness of polynomial mappings, Math. Ann., 315 (1999) 1-35.