The super period map and the projectedness of supermoduli space

Abstract: In 2014, Donagi and Witten proved that supermoduli spaces $\mathfrak{M}_g$ of genus $g$ super Riemann surfaces are not projected for genus $g \geq 5$. In joint work with Ron Donagi, we show that $\mathfrak{M}_g$ is projected, for all genus $g$, away from the so-called bad divisor. In other words, we show that the complement $U_g$ of $\mathcal{B} \subset \mathfrak{M}_g$ is a projected open subscheme of $\mathfrak{M}_g$. Furthermore, at least in genus $g = 2$ and $g = 3$, we show that the super period map defines a projection $U_g \to U_{g,\mathrm{bos}}$.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

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