An epimorphic subgroup arising from Roberts' counterexample

Details An epimorphic subgroup arising from Roberts' counterexample An epimorphic subgroup arising from Roberts' counterexample

2011-02-17

arxiv.org/abs/1102.3543v2

Indagationes Mathematicae, vol. 23 (2012), no. 1-2, 10-18

Mathematics

Algebraic Geometry

v2: 9 pages, small corrections

Scientific paper

10.1016/j.indag.2011.09.009

In 1994, based on Roberts' counterexample to Hilbert's fourteenth problem, A'Campo-Neuen constructed an example of a linear action of a 12-dimensional commutative unipotent group H_0 on a 19-dimensional vector space V such that the algebra of invariants k[V]^{H_0} is not finitely generated. We consider a certain extension H of H_0 by a one-dimensional torus and prove that H is epimorphic in SL(V). In particular, the homogeneous space SL(V)/H provides a new example of a homogeneous space with epimorphic stabilizer that admits no projective embeddings with small boundary.

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