论文标题
用于理性属2曲线的模量具有实际乘法5
Moduli for rational genus 2 curves with real multiplication for discriminant 5
论文作者
论文摘要
具有规定的实际乘法（RM）的主要极化的Abelian表面被某些Hilbert模块化表面参数化。因此，有理属2曲线通过其雅各布人对应于希尔伯特模块化表面上的理性点，但相反的是不正确的。我们给出了一个简单的通用描述，说明哪些有理模量点对应于有理曲线，并给出了相关的Weierstrass模型，在RM的情况下，$ \ Mathbb {q}（\ sqrt {5}）$的整数rm。为了证明这一点，我们为减少多项式环的二次形式提供了一些技术。
Principally polarized abelian surfaces with prescribed real multiplication (RM) are parametrized by certain Hilbert modular surfaces. Thus rational genus 2 curves correspond to rational points on the 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 $\mathbb{Q}(\sqrt{5})$. To prove this, we provide some techniques for reducing quadratic forms over polynomial rings.
