Abelian surfaces of GL2-type as Jacobians of curves
Abstract
We study the set of isomorphism classes of principal polarizations on abelian varieties of GL2-type. As applications of our results, we construct examples of curves C, C'/ of genus two which are nonisomorphic over and share isomorphic unpolarized modular Jacobian varieties over ; we also show a method to obtain genus two curves over whose Jacobian varieties are isomorphic to Weil's restriction of quadratic -curves, and present examples.
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