Proper twin-triangular Ga-actions on A^4 are translations

Abstract : An additive group action on an affine 3 -space over a complex Dedekind domain A is said to be twin-triangular if it is generated by a locally nilpotent derivation of A[y,z,t] of the form rd/dy+p(y)d/dz + q(y)d/dt , where r belongs to A and p,q belong to A[y] . We show that these actions are translations if and only if they are proper. Our approach avoids the computation of rings of invariants and focuses more on the nature of geometric quotients for such actions.
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https://hal.archives-ouvertes.fr/hal-00627521
Contributor : Adrien Dubouloz <>
Submitted on : Wednesday, September 28, 2011 - 7:46:57 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Thursday, December 29, 2011 - 2:31:10 AM

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  • HAL Id : hal-00627521, version 1
  • ARXIV : 1109.6302

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Adrien Dubouloz, David Finston. Proper twin-triangular Ga-actions on A^4 are translations. 2011. ⟨hal-00627521⟩

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