The Coleman-Oort conjecture: reduction to three key cases
Ben Moonen
TL;DR
This paper reduces the Coleman-Oort conjecture to three specific cases and proves its validity on the hyperelliptic locus for genus at least 8, extending previous results.
Contribution
It narrows down the conjecture to three key cases and extends its verification to higher genus hyperelliptic loci.
Findings
Conjecture reduced to three cases
Verification on hyperelliptic locus for g ≥ 8
Extension of Lu and Zuo's result
Abstract
We show that the Coleman-Oort conjecture can be reduced to three particular cases. As an application we extend a result of Lu and Zuo, to the effect that for g at least 8 the Coleman-Oort conjecture is true on the hyperelliptic locus.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry