## Complete moduli in the presence of semiabelian group action

Venue: | Ann. of Math |

Citations: | 58 - 5 self |

### BibTeX

@ARTICLE{Alexeev_completemoduli,

author = {Valery Alexeev},

title = {Complete moduli in the presence of semiabelian group action},

journal = {Ann. of Math},

year = {},

pages = {611--708}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. 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 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 secondary polytope and coincides with the

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