Polyhedral algebras, arrangements of toric varieties, and their groups, by Winfried Bruns and Joseph Gubeladze

We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric varieties. It is shown that for wide classes of complexes they are generated by toric actions, elementary transformations and symmetries of the underlying complex. The main results extend our previous work for single polytopes (#203 in this server).

In conjunction with #203 the present paper establishes a polyhedral generalization of classical K-theoretical objects -- the general linear group GL_n(k) and its elementary subgroup E_n(k) (k a field). Naturally there arises a question: is there a further analogy with K-theory that might lead to a polyhedral K-theory? Already for low dimensional K-groups this question suggests challenging open problems.

Winfried Bruns <Winfried.Bruns@mathematik.uni-osnabrueck.de>
Joseph Gubeladze <>