A family of arithmetic surfaces of genus 3.
type: Item
instance of: scholarly article
title: A family of arithmetic surfaces of genus 3.
zbMATH Open document ID: 1058.14038
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: The author studies a family of the genus 3 curves defined by \[ C_n: Y^4= X^4- (4n- 2)X^2+ 1 \] from the viewpoint of arithmetical and Arakelov geometry. Firstly, the author shows, using his previous result on the automorphism group of \(C_n\), that the Jacobian of \(C_n\) splits as a product of elliptic curves. Using this fact, he finds the stable models of the curves \(C_n\) and studies their arithmetic and geometric properties. Combining these, the author gives explicit expressions of the modular height and the self-intersecction of the dualizing sheaf of the curves \(C_n\).
reviewed by: Masanori Morishita
Mathematics Subject Classification ID: 14G40
Mathematics Subject Classification ID: 11G30
zbMATH DE Number: 2101123
zbMATH Keywords: genus 3 curves
zbMATH Keywords: modular height
zbMATH Keywords: self-intersection of the dualizing sheaf
author: Jordi Guárdia
MaRDI profile type: Publication
full work available at URL: pjm.2003.212.71
OpenAlex ID: W2021581305
DOI: 10.2140/PJM.2003.212.71
description: scientific article; zbMATH DE number 2101123