The Abel Jacobi map for Mumford Curves via Integration
Iago Gin\'e, Xavier Xarles
TL;DR
This paper constructs the Abel-Jacobi map for Mumford curves over non-archimedean fields using multiplicative integrals within Berkovich geometry, and explores related tropical geometry results.
Contribution
It introduces a new construction of the Abel-Jacobi map for Mumford curves via multiplicative integrals in Berkovich spaces, linking non-archimedean geometry and tropical measures.
Findings
Established the Abel-Jacobi map for Mumford curves in Berkovich spaces.
Proved results connecting graphs and measures in tropical geometry.
Enhanced understanding of non-archimedean analytic geometry techniques.
Abstract
We construct the Abel-Jacobi map for Mumford curves over any complete non-archimedean field, using multiplicative integrals and in the setting of Berkovich analytic geometry. Along the way, we proof some results concerning graphs and mesures related to tropical geometry.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds