# Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties - Mathematics > Algebraic Geometry

Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this paper, we define a generalized arithmetic-geometric mean $\mu g$among $2^g$ terms motivated by $2\tau$-formulas of theta constants. By usingThomae-s formula, we give two expressions of $\mu g$ when initial terms satisfysome conditions. One is given in terms of period integrals of a hyperellipticcurve $C$ of genus $g$. The other is by a period integral of a certainCalabi-Yau $g$-fold given as a double cover of the $g$-dimensional projectivespace $\mathbf{P}^g$.

Author: ** Keiji Matsumoto, Tomohide Terasoma**

Source: https://arxiv.org/