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An epimorphic subgroup arising from Roberts' counterexample
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.Comment: v2: 9 pages, small correction
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