# Zhengning Hu: A computation of Sym^2(\Pic(\Hbar_g))

**Time: **
Thu 2021-09-30 15.30 - 16.30

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Participating: **
Zhengning Hu (University of Missouri)

**Abstract:** We denote by \(\overline{\mathcal{H}}_g\) the closure of the hyperelliptic locus in the moduli space of stable curves of genus *g*. We consider the map \(\operatorname{Sym}^2(\operatorname{Pic}(\overline{\mathcal{H}}_g)) \to \mathrm{CH}^2(\overline{\mathcal{H}}_g)\) and prove the kernel of the map is generated by a single relation. Moreover, the relation depends on the parity of *g*, but otherwise the relation has a simple recursive form.