A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves

@article{Mulase1991ANS,
  title={A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves},
  author={Motohico Mulase},
  journal={Journal of Differential Geometry},
  year={1991},
  volume={34},
  pages={651-680}
}
  • M. Mulase
  • Published 1991
  • Mathematics
  • Journal of Differential Geometry
A set of super-commuting vector fields is defined on the super Grassmannians. A characterization of the Jacobian varieties of super curves (super Schottky problem) is established in the following manner: Every finite dimensional integral manifold of these vector fields has a canonical structure of the Jacobian variety of an algebraic super curve, and conversely, the Jacobian variety of an arbitrary algebraic super curve is obtained in this way. The vector fields restricted on the super… 
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References

SHOWING 1-10 OF 23 REFERENCES
The geometry of the super KP flows
A supersymmetric generalization of the Krichever map is used to construct algebro-geometric solutions to the various super Kadomtsev-Petviashvili (SKP) hierarchies. The geometric data required
Solvability of the super KP equation and a generalization of the Birkhoff decomposition
SummaryThe unique solvability of the initial value problem for the total hierarchy of the super Kadomtsev-Petviashvili system is established. To prove the existence we use a generalization of the
SUPER KRICHEVER FUNCTOR
A supersymmetric generalization of the Krichever map is proposed. This map assigns injectively a point of an infinite dimensional super Grassmannian to a set of geometric data consisting of an
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 for
Gauge Field Theory and Complex Geometry
Geometrical Structures in Field Theory.- 1. Grassmannians, Connections, and Integrability.- 2. The Radon-Penrose Transform.- 3. Introduction to Superalgebra.- 4. Introduction to Supergeometry.- 5.
Cohomological structure in soliton equations and Jacobian varieties
On etudie la structure des orbites du systeme dynamique definie par la hierarchie KP totale. On montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une
Geometry of superconformal manifolds
The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the fermion string theory and, in particular, they are useful for
Loop groups and equations of KdV type
On decrit une construction qui attribue une solution de l'equation de Korteweg-de Vries a chaque point d'un certain grassmannien de dimension infinie. On determine quelle classe on obtient par cette
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