Article

# An epimorphic subgroup arising from Roberts' counterexample

02/2011; DOI:10.1016/j.indag.2011.09.009
Source: arXiv

ABSTRACT 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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### Keywords

19-dimensional vector space

A'Campo-Neuen

algebra

certain extension H

epimorphic stabilizer

Hilbert's fourteenth problem

homogeneous space

homogeneous space SL(V)/H

linear action

one-dimensional torus