Complete Moduli in the Presence of Semiabelian Group Action
نویسندگان
چکیده
I prove the existence, and describe the structure, of moduli space of pairs (P,Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component containing a projective toric variety is described by a configuration of several polytopes, the main one of which is the secondary polytope. On the other hand, the component containing a principally polarized abelian variety provides a moduli compactification of Ag. The main irreducible component of this compactification is described by an “infinite periodic” analog of the secondary polytope and coincides with the toroidal compactification of Ag for the second Voronoi decomposition.
منابع مشابه
On Semiabelian Groups
Recall that a group is called semiabelian if it is generated by its normal cyclic subgroups [6]. The class of semiabelian groups is a very natural generalization of the wellknown class of Dedekind groups (the groups in which all cyclic subgroups are normal). In the paper [6] Venzke showed that these groups could play a major role in the theory of supersoluble finite groups. Based on the notion ...
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