An illustration of a Shioda-Inose structure
Francois-Xavier Machu
TL;DR
This paper explores the Shioda-Inose structure of Jacobians of genus-2 curves, focusing on elliptic subcovers, and determines Mordell-Weil groups and lattices for specific semistable fibrations with four singular fibers.
Contribution
It provides a detailed analysis of the Shioda-Inose structure in genus-2 Jacobians and explicitly computes Mordell-Weil groups and lattices for certain semistable fibrations.
Findings
Determined Mordell-Weil groups for specific fibrations.
Analyzed the lattice structures associated with the Jacobians.
Connected elliptic subcovers to the Shioda-Inose structure.
Abstract
We investigate the Shioda-Inose structure of the Jacobian of a smooth complex genus-2 curve C arising from its degree-2 elliptic subcovers and determine the Mordell-Weil groups and lattices in the case of a semistable fibration having exactly four singular fibers.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry