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Linearizing some ℤ/2ℤ actions on affine space

In: Algebraic Geometry

Author

Listed:
  • Jerzy Jurkiewicz

    (University of Warsaw, Institute of Mathematics)

Abstract

Let V be the affine space k n over an algebraically closed field k, G a linearly reductive group and A: G×V → V a group action with a fixed point, say the origin. Then for all g ∈ G let me denote by A(g) the corresponding automorphism of V. We have $$A(g) = L(g) + D(g)$$ where L(g), D(g)∈ End V, L(g) linear and D(g) the sum of terms of higher degrees. Let me recall the well known linearization problem: is the action A linearizable, i.e. conjugated to the linear action L: G ×V →V (see e.g. [B] and [K])? Recently counter-examples have been found, see [S] and [K + S], so it is reasonable to study additional assumptions on the action A. One of them is considered in the present paper.

Suggested Citation

  • Jerzy Jurkiewicz, 1990. "Linearizing some ℤ/2ℤ actions on affine space," Springer Books, in: H. Kurke & J. H. M. Steenbrink (ed.), Algebraic Geometry, pages 243-245, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0685-3_11
    DOI: 10.1007/978-94-009-0685-3_11
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