## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- 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

### Moduli spaces and locally symmetric varieties

#### 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

**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