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<p>This paper gives a criterion for a moduli point to be a point of non-transversal intersection of the hyperelliptic locus and the supersingular locus in the Siegel moduli stack <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {A}_3 \times \mathbb {F}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="fraktur">A</mi> <mn>3</mn> </msub> <mo>×</mo> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. It is shown that for infinitely many primes <i>p</i> there exists such a point.</p>

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On the non-transversality of the hyperelliptic locus and the supersingular locus for \(g=3\)

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  • 发表日期：

    2026年5月2日

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  • Andreas Pieper

摘要

This paper gives a criterion for a moduli point to be a point of non-transversal intersection of the hyperelliptic locus and the supersingular locus in the Siegel moduli stack \(\mathfrak {A}_3 \times \mathbb {F}_p\) A 3 × F p . It is shown that for infinitely many primes p there exists such a point.