Geometry of equivariant compactifications of Gⁿ_a

1999/02/11 by Brendan Hassett, Yuri Tschinkel, Hassett, Brendan +1 · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9902073

22 pages, LaTeX

arxiv created 1999/02/11 · arxiv updated 2009/11/30

Abstract

Equivariant compactifications of reductive groups can be described by combinatorial data. On the other hand, equivariant compactifications of the additive group Gⁿ_a are more complicated in at least two respects. First, they often admit moduli. Second, even simple varieties (like projective spaces) admit many different structures as equivariant compactifications of the additive group. We give a dictionary relating Artinian local rings, certain systems of partial differential equations, and equivariant compactifications of Gⁿ_a. As an application, we classify the structures on varieties like projective spaces, ruled surfaces, and certain threefolds. We consider these results as a first step in a systematic study of Gⁿ_a-equivariant birational geometry.

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