Compactifications defined by arrangements I: The Ball Quotient case
By E. Looijenga. 2001
71 citations recorded by the source corpus.
We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric invariant theory. We illustrate this with the moduli spaces of smooth quartic curves and rational elliptic surfaces.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/787b6897634dd774c042a948b918bf9fc360e569
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In Geometry and Topology
- E. Looijenga
- David E. Speyer
- Nicholas Proudfoot
- W. Couwenberg
- G. Heckman
- Igor Dolgachev
- Eric Katz
- Lauren K. Williams
In Mathematical Physics
- E. Looijenga
- David E. Speyer
- Nicholas Proudfoot
- W. Couwenberg
- G. Heckman
- Igor Dolgachev
- Alexander Perry
- R. Laza
Citations in the corpus
- A Broken Circuit Ring (2004, background): “The ring R(L) also appears as a cohomology ring in [PW], and as the homogeneous coordinate ring of a projective variety in [ Lo , 3.1].”
- Geometric Structures on the Complement of a Projective Arrangement (2003, background): “In [16] a systematic study was made of algebras of meromorphi c automorphic forms of the type under consideration here.”
- Compactications defined by arrangements II: locally symmetric varieties of type IV (2002, background): “The line I determines a realization of D as a tube domain: the projection D → πID is a GI -equivariant isomorphism and πID can be characterized as a subset of P(V/I) as follows.”