2022/12/21 by Francesc Fité, Fité, Francesc, Enric Florit +3
Mathematics · Medicine · Computer Science · #Advanced Differential Equations and Dynamical Systems #Multiple Myeloma Research and Treatments #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2212.11102
The main result of [FG20] classifies the 92 geometric endomorphism algebras of geometrically split abelian surfaces defined over Q. We show that 54 of them arise as geometric endomorphism algebras of Jacobians of genus 2 curves defined over Q, and that the remaining 38 do not. In particular, we exhibit 38 examples of Qbar-isogeny classes of abelian surfaces defined over Q that do not contain any Jacobian of a genus 2 curve defined over Q, and for each of the 54 algebras that do arise we exhibit a curve realizing them.