Year: 2024
Type: article
Abstract: Principally polarized abelian surfaces with prescribed real multiplication (RM) are parametrized by certain Hilbert modular surfaces. Thus rational genus 2 curves with RM correspond to rational points on Hilbert modular surfaces via their Jacobians, but the converse is not true. We give a simple generic description of which rational moduli points correspond to rational curves, as well as give associated Weierstrass models, in the case of RM by the ring of integers of ℚ ( 5 ) . To prove this, we provide some techniques for reducing quadratic forms over polynomial rings.
DOI: 10.5802/jtnb.1286
Authors: Alex Cowan, Kimball Martin
Institutions: University of Waterloo, University of Oklahoma
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404302391