由Roberts反例产生的满同态子群
An epimorphic subgroup arising from Roberts' counterexample
摘要：
在1994年，基于希尔伯特第十四问题的Roberts反例，A 'Campo-Neuen构造了一个12维交换幂幺群H_0在19维向量空间V上的线性作用的例子，使得不变量代数k[V]^{H_0}不是非线性生成的。考虑H_0的一维环面扩张H，证明了H在SL（V）中满射.特别地，齐性空间SL（V）/H提供了一个新的例子，证明了具有满射稳定子的齐性空间不允许有小边界的射影嵌入.
英文摘要：
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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