The Torelli locus and special subvarieties
Ben Moonen, Frans Oort
TL;DR
This paper investigates the Torelli locus within the moduli space of abelian varieties, focusing on special Shimura subvarieties, their construction, related conjectures, and recent advancements in understanding their properties.
Contribution
It reviews the construction of non-trivial Shimura subvarieties in the Torelli locus and discusses current conjectures, techniques, and progress in the field.
Findings
Construction of non-trivial examples of special subvarieties
Discussion of conjectures related to the Torelli locus
Overview of recent progress and techniques
Abstract
We study the Torelli locus T_g in the moduli space A_g of abelian varieties. We consider special subvarieties (Shimura subvarieties) contained in the Torelli locus. We review the construction of some non-trivial examples, and we discuss some conjectures, techniques and recent progress.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Coding theory and cryptography