Gale duality and homogeneous toric varietiesстатья
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Дата последнего поиска статьи во внешних источниках: 10 августа 2018 г.
Аннотация:A non-degenerate toric variety X is called S-homogeneous if the subgroup
of the automorphism group Aut(X) generated by root subgroups acts on X transitively.
We prove that maximal S-homogeneous toric varieties are in bijection with pairs (P, A),
where P is an abelian group and A is a finite collection of elements in P such that A generates
the group P and for every a ∈ A the element a is contained in the semigroup generated
by A \ {a}. We show that any non-degenerate homogeneous toric variety is a big open
toric subset of a maximal S-homogeneous toric variety. In particular, every homogeneous
toric variety is quasiprojective. We conjecture that any non-degenerate homogeneous toric
variety is S-homogeneous.