|Arrangements and Moduli Spaces|
Abstract: An arrangement in a projective space is a finite collection of hyperplanes of that space. This notion has a natural extension to the case of a torus embedding or an abelian variety. And also to the case of the Baily-Borel compactification of an arithmetic quotient of complex ball or of a type IV domain. There is a uniform way of modifying such a variety in terms of the given arrangement, which in the case of the three coordinate lines in the projective plane boils down to the standard Cremona transformation. Surprisingly, many GIT quotients that have an interpretation as a moduli space of varieties for which a Torelli theorem holds can so be obtained (in one of these settings). For instance, this applies to the moduli spaces of quartic curves, sextic curves, quartic surfaces, Enriques surfaces, rational elliptic surfaces. There are also interesting examples in singularity theory.
|Web page: Alexandru I. Suciu||Comments to: email@example.com|
|Created: March 29, 2001||URL: http://www.math.neu.edu/bhmn/looijenga.html|