Higher-weight Jacobians for complex varieties of maximal Picard number

Abstract: This talk is about my work with Max Lieblich where we define and study Jacobians of Hodge structures with weight greater than 1. Jacobians of weight 2 or "2-Jacobians" naturally come up in the context of the Brauer group and the Tate conjecture, and were previously studied in a special case by Beauville in his work on surfaces of maximal Picard number. I will explain how we compute higher-weight Jacobians (as complex tori) for certain special classes of complex varieties, namely abelian varieties of maximal Picard rank or singular K3 surfaces. Surprisingly, these $m$-Jacobians are algebraic for all values of $m$.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar