Compactifications defined by arrangements II: locally symmetric varieties of type IV
| dc.creator | Looijenga, Eduard | |
| dc.date | 2002-01-22 | |
| dc.date | 2002-04-26 | |
| dc.date.accessioned | 2026-07-07T04:46:03Z | |
| dc.date.available | 2026-07-07T04:46:03Z | |
| dc.description | We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of type IV determines such a completion canonically. This completion admits a natural contraction that leaves the complement of the arrangement untouched. The resulting completion of the arrangement complement is very much like a Baily-Borel compactification: it is the proj of an algebra of meromorphic automorphic forms. When that complement has a moduli space interpretation, then what we get is often a compactification obtained by means of geometric invariant theory. We illustrate this with several examples: moduli spaces of polarized $K3$ and Enriques surfaces and the semi-universal deformation of a triangle singularity. We also discuss the question when a type IV arrangement is definable by an automorphic form. | |
| dc.description | The section on arrangements on tube domains has beeen expanded in order to make a connection with a conjecture of Gritsenko and Nikulin. Also added: a list of notation and some references. Finally some typo's corrected and a few minor changes made in notation | |
| dc.identifier | https://arxiv.org/abs/math/0201218 | |
| dc.identifier | http://arxiv.org/abs/math/0201218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63183 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J15; 32N15 | |
| dc.title | Compactifications defined by arrangements II: locally symmetric varieties of type IV | |
| dc.type | text |