论文标题
Abelian表面模量空间的算术体积
The arithmetic volume of the moduli space of abelian surfaces
论文作者
论文摘要
令$ \ Mathcal {a} _g $表示主要偏光尺寸的尺寸$ g $的模量堆栈。 $ \ overline {\ Mathcal {a}} _ g $的算术高度或算术音量定义为$ \ + edlineLline {\ Mathcal {a}} _ g $的算术型hodge bundle $ \overlineΩ_g$。在1999年，库恩证明了$ \ overline {\ mathcal {a}} _ 1 $的算术音量的公式。在本文中，我们将他的结果概括为$ g = 2 $。
Let $\mathcal{A}_g$ denote the moduli stack of principally polarized abelian varieties of dimension $g$. The arithmetic height, or arithmetic volume, of $\overline{\mathcal{A}}_g$, is defined to be the arithmetic degree of the metrized Hodge bundle $\overlineω_g$ on $\overline{\mathcal{A}}_g$. In 1999, Kühn proved a formula for the arithmetic volume of $\overline{\mathcal{A}}_1$ in terms of special values of the Riemann zeta function. In this article, we generalize his result to the case $g=2$.
