Siegel modular forms and the gonality of curves
N.I. Shepherd-Barron
TL;DR
This paper proves that no stable Siegel modular form vanishes on the trigonal locus across all moduli spaces of curves, highlighting a fundamental limitation in the behavior of such forms.
Contribution
It establishes a non-existence result for stable Siegel modular forms vanishing on the trigonal locus in all moduli spaces.
Findings
No stable Siegel modular form vanishes on the trigonal locus universally.
The result constrains the possible modular forms related to curve gonality.
Provides insight into the structure of moduli spaces and modular forms.
Abstract
There is no stable Siegel modular form that vanishes on the trigonal locus in every moduli space of curves.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals