Moduli spaces of abstract and embedded Kummer varieties

@article{Galeotti2018ModuliSO,
  title={Moduli spaces of abstract and embedded Kummer varieties},
  author={Mattia Galeotti and Sara Perna},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
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… 
1 Citations
On the cone of effective surfaces on $\overline{\mathcal A}_3$
We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification $\overline{\mathcal A}_3$ of the moduli space ${\mathcal A}_3$ of complex

References

SHOWING 1-10 OF 21 REFERENCES
Perfect forms and the moduli space of abelian varieties
Toroidal compactifications of the moduli space A g , or the stack A g , of principally polarized abelian g-folds have been constructed over C in [AMRT] and over any base in [FC]. Roughly speaking,
16, 6 Configurations and Geometry of Kummer Surfaces in P3
This monograph studies the geometry of a Kummer surface in ${\mathbb P}^3_k$ and of its minimal desingularization, which is a K3 surface (here $k$ is an algebraically closed field of characteristic
Equations Defining Abelian Varieties
We shall start this chapter by proving “theta relations,” i.e., relations between theta functions. More precisely, we shall be interested in polynomial relations between θm(τ, z), θm(τ, 0) with
Principally polarized semi-abelic varieties of small torus rank, and the Andreotti-Mayer loci
We obtain, by a direct computation, explicit descriptions of all principally polarized semi-abelic varieties of torus rank up to 3. We describe the geometry of their symmetric theta divisors and
Geometry of theta divisors --- a survey
We survey the geometry of the theta divisor and discuss various loci of principally polarized abelian varieties (ppav) defined by imposing conditions on its singularities. The loci defined in this
The Universal Kummer Threefold
TLDR
This work develops classical themes such as theta functions and Coble's quartic hypersurfaces using current tools from combinatorics, geometry, and commutative algebra to compute defining polynomials for genus-3 moduli spaces.
Some equations for the universal Kummer variety
We give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one obtains equations
Twisted Bundles and Admissible Covers
Abstract We study the structure of the stacks of twisted stable maps to the classifying stack of a finite group G—which we call the stack of twisted G-covers, or twisted G-bundles. For a suitable
Degeneration of Abelian varieties
I. Preliminaries.- II. Degeneration of Polarized Abelian Varieties.- III. Mumford's Construction.- IV. Toroidal Compactification of Ag.- V. Modular Forms and the Minimal Compactification.- VI.
Bookreview Geometry of algebraic curves. Volume II (Grundlehren der mathematischen Wissenschaften, 268)
Volume I came with many exercises, which not only helped the reader to absorb the material, but often also played an educational, ‘Bourbaki-esque’ role by pointing the reader to many interesting
...
1
2
3
...