---
- CiteKey: "Ale04"
- Type: report
- Title: "Complete moduli in the presence of semiabelian group action," 
- Author: "Alexeev, Valery;"  
- Publisher: "arXiv,"
- Year: 2004 
- Keywords: "14K10"; "Mathematics - Algebraic Geometry"
---

# Complete moduli in the presence of semiabelian group action

## Meta

- **URL**: <http://arxiv.org/abs/math/9905103>
- **URI**: <http://zotero.org/users/1049732/items/TLMCDDS7>
- **Local File**: [arXiv Fulltext PDF](file:///home/zack/Zotero/storage/4HVLXWJ5/Alexeev%20-%202004%20-%20Complete%20moduli%20in%20the%20presence%20of%20semiabelian%20gro.pdf); [arXiv.org Snapshot](file:///home/zack/Zotero/storage/66UDN92B/9905103.html)
- **Open in Zotero**: [Zotero](zotero://select/library/items/TLMCDDS7)

## Abstract

I prove the existence, and describe the structure, of moduli space of pairs $(p,\Theta)$ 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 $A_g$. 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 $A_g$ for the second Voronoi decomposition.

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