2013/08/23 by Samuel Grushevsky, Martin Möller, Grushevsky, Samuel +1
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1308.5155
openalex publication_date 2013/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an infinite number of Shimura curves contained in the locus of\nhyperelliptic Jacobians of genus 3. In the opposite direction, we show that in\ngenus 3 the only possible non-complete (in the moduli space of abelian\nthreefolds) Kuga curves contained in the hyperelliptic locus have the same\ndegeneration data as that of the examples we construct.\n The locus of genus 3 hyperelliptic Jacobians is a divisor within the moduli\nspace of principally polarized abelian threefolds, and our result demonstrates\nthe techniques we develop more generally for dealing with Shimura curves\ncontained within a divisor in the moduli space of abelian varieties.\n