Heights of abelian varieties, and tropical geometry

Abstract: We give a formula which, for a principally polarized abelian variety $(A,\lambda)$ over the field of algebraic numbers, relates the stable Faltings height of $A$ with the N\'eron-Tate height of a symmetric theta divisor on $A$. Our formula involves invariants arising from tropical geometry. We also discuss the case of Jacobians in some detail, where graphs and electrical networks will play a key role. (Based on joint works with Robin de Jong.)

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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