The weighted moduli spaces of sextics
Lubjana Beshaj, Scott Guest

TL;DR
This paper investigates the distribution of fine moduli points in the moduli space of genus two curves using weighted moduli height, establishing bounds and creating a database of curves with small height to analyze their properties.
Contribution
It introduces bounds on weighted moduli height for genus two curves and constructs a database to study the distribution of fine moduli points based on this height.
Findings
Approximately 30% of points with small height are fine moduli points.
Established an upper bound for weighted moduli height in terms of naive height.
Created a database of genus two curves over Q with small weighted moduli height.
Abstract
We use the weighted moduli height as defined in \cite{sh-h} to investigate the distribution of fine moduli points in the moduli space of genus two curves. We show that for any genus two curve with equation , its weighted moduli height , where is the minimal naive height of the curve as defined in \cite{height}. Based on the weighted moduli height we create a database of genus two curves defined over with small and show that for small such height () about 30% of points are fine moduli points.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry
