## Abstract

For a group G acting on an affine variety X, the separating variety is the closed subvariety of X × X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations _{V n} of dimension n + 1 of the additive group of a field of characteristic zero, and decompose the separating variety into the union of irreducible components. We show that if n is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension n + 2, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension n + 1. We conclude that in these cases, there are no polynomial separating algebras.

Original language | English |
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Pages (from-to) | 269-280 |

Number of pages | 12 |

Journal | Journal of Algebra |

Volume | 377 |

DOIs | |

Publication status | Published - 1 Mar 2013 |

## Keywords

- Basic actions
- Invariant theory
- Locally nilpotent derivations
- Separating invariants
- Weitzenböck derivations