Moduli spaces of abstract and embedded Kummer varieties

  title={Moduli spaces of abstract and embedded Kummer varieties},
  author={Mattia Galeotti and Sara Perna},
  journal={arXiv: Algebraic Geometry},
In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack $\mathcal K^{\text{abs}}_g$ of abstract Kummer varieties and the second one is the stack $\mathcal K^{\text{em}}_g$ of embedded Kummer varieties. We will prove that $\mathcal K^{\text{abs}}_g$ is a Deligne-Mumford stack and its coarse moduli space is isomorphic to $\boldsymbol A_g$, the coarse moduli space of principally polarized abelian varieties of dimension $g$. On the other… 
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