Moduli and periods of supersymmetric curves

@article{Codogni2019ModuliAP,
  title={Moduli and periods of supersymmetric curves},
  author={Giulio Codogni and Filippo Viviani},
  journal={Advances in Theoretical and Mathematical Physics},
  year={2019}
}
Supersymmetric curves are the analogue of Riemann surfaces in super geometry. We establish some foundational results about complex Deligne-Mumford superstacks, and we then prove that the moduli superstack of supersymmetric curves is a smooth complex Deligne-Mumford superstack. We then show that the superstack of supersymmetric curves admits a coarse complex superspace, which, in this case, is just an ordinary complex space. In the second part of this paper we discuss the period map. We remark… Expand
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References

SHOWING 1-10 OF 91 REFERENCES
Global structures for the moduli of (punctured) super riemann surfaces
Abstract A fine moduli superspace for algebraic super Riemann surfaces with a level- n structure is constructed as a quotient of the split superscheme of local spin-gravitivo fields by an etaleExpand
Moduli stacks of maps for supermanifolds
We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry ofExpand
Pluri-Canonical Models of Supersymmetric Curves
This paper is about pluri-canonical models of supersymmetric (susy) curves. Susy curves are generalisations of Riemann surfaces in the realm of super geometry. Their moduli space is a key object inExpand
Supercurves, their Jacobians, and super KP equations
We study the geometry and cohomology of algebraic super curves, using a new contour integral for holomorphic differentials. For a class of super curves (``generic SKP curves'') we define a periodExpand
The super period matrix with Ramond punctures
Abstract We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2 r Ramond punctures, we define,Expand
Super Atiyah classes and obstructions to splitting of supermoduli space
The first obstruction to splitting a supermanifold S is one of the three components of its super Atiyah class, the two other components being the ordinary Atiyah classes on the reduced space M of theExpand
Regularity of the superstring supermeasure and the superperiod map
The supermeasure whose integral is the genus $g$ vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the corresponding evenExpand
Graded Riemann surfaces
There has been a lot of activity directed at describing super Riemann surfaces and the super Teichmuller spaces that classify them. Most descriptions use a subcategory ofG∞-supermanifolds in whichExpand
Supertori are algebraic curves
Super Riemann surfaces of genus 1, with arbitrary spin structures, are shown to be the sets of zeroes of certain polynomial equations in projective superspace. We conjecture that the same is true forExpand
Super Riemann surfaces: Uniformization and Teichmüller theory
Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstringExpand
...
1
2
3
4
5
...