Fano Shimura varieties with mostly branched cusps

TL;DR

This paper classifies the geometric types of certain Shimura varieties' compactifications, showing they can be Fano, Calabi-Yau, or have ample canonical divisors, with applications to moduli spaces of Enriques surfaces.

Contribution

It establishes new classifications of Shimura varieties' compactifications and explores their geometric properties, including novel examples like moduli spaces of unpolarized Enriques surfaces.

Findings

Shimura varieties' compactifications can be Fano, Calabi-Yau, or have ample canonical divisors.

Provides new examples of moduli spaces with these properties.

Discusses applications and variants of the main results.

Abstract

We prove that the Satake-Baily-Borel compactification of certain Shimura varieties are Fano varieties, Calabi-Yau varieties or have ample canonical divisors with mild singularities. We also prove some variants statements, give applications and discuss various examples including new ones, for instance, the moduli spaces of unpolarized (log) Enriques surfaces.