A note on Shimura subvarieties in the hyperelliptic Torelli locus
Ke Chen, Xin Lu, and Kang Zuo
TL;DR
This paper proves that for curves of genus at least 8, there are no positive-dimensional Shimura subvarieties contained generically in the hyperelliptic Torelli locus, supporting an analogue of Oort's conjecture.
Contribution
It establishes the non-existence of certain Shimura subvarieties in the hyperelliptic Torelli locus for high genus curves, extending Oort's conjecture to the hyperelliptic case.
Findings
No positive-dimensional Shimura subvarieties in the hyperelliptic Torelli locus for genus ≥ 8
Supports the hyperelliptic analogue of Oort's conjecture
Advances understanding of the structure of Torelli loci in algebraic geometry
Abstract
We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analogue of Oort's conjecture in the hyperelliptic case.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Finite Group Theory Research