Mathematics Colloquia and Seminars

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I'll start by defining the Chow ring, which is an important invariant of a scheme (or stack). Next, I will define the Picard variety and Picard stack of a curve, and then introduce their universal versions J^d_g and \mathscr{J}^d_g over the moduli space of curves M_g. Recently, progress has been made studying the Chow ring of M_g in low genus by stratifying the moduli space by gonality (the minimal degree of a map to P^1). The smallest piece in this stratification is the hyperelliptic locus. Motivated by this, I'll present several results about the restriction of \mathscr{J}^d_g to the hyperelliptic locus, denoted \mathscr{J}^d_{2,g}.