Advanced Studies in Pure Mathematics

Moduli spaces and locally symmetric varieties

Eduard Looijenga

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This survey paper is about moduli spaces in algebraic geometry for which a period map gives that space the structure of a (possibly incomplete) locally symmetric variety and about their natural compactifications. We outline the Baily-Borel compactification for such varieties, and show that it usually differs from the compactifications furnished by the standard techniques in algebraic geometry. It turns out however, that a reconciliation is possible by means of a generalization of the Baily-Borel construction for the class of incomplete locally symmetric varieties that occur here.

The emphasis is here on moduli spaces of varieties other than that of polarized abelian varieties.

Article information

Source
Development of Moduli Theory — Kyoto 2013, O. Fujino, S. Kondō, A. Moriwaki, M. Saito and K. Yoshioka, eds. (Tokyo: Mathematical Society of Japan, 2016), 33-75

Dates
Received: 9 April 2014
Revised: 8 October 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538622429

Digital Object Identifier
doi:10.2969/aspm/06910033

Mathematical Reviews number (MathSciNet)
MR3586506

Zentralblatt MATH identifier
1369.14044

Subjects
Primary: 14J15: Moduli, classification: analytic theory; relations with modular forms [See also 32G13] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 32N15: Automorphic functions in symmetric domains

Keywords
Baily-Borel compactification moduli

Citation

Looijenga, Eduard. Moduli spaces and locally symmetric varieties. Development of Moduli Theory — Kyoto 2013, 33--75, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/06910033. https://projecteuclid.org/euclid.aspm/1538622429


Export citation