Compactness for holomorphic supercurves
Copyright policy )Compactness for holomorphic supercurves
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of holomorphic supercurves and prove that, in important cases, every such sequence has a convergent subsequence provided that a suitable extension of the classical energy is uniformly bounded. This is a version of Gromov compactness. Finally, we introduce a topology on the moduli spaces enlarged by the limiting objects which makes these spaces compact and metrisable.
38 pages
- Humboldt-Universität zu Berlin Germany
Global theory of symplectic and contact manifolds, holomorphic curves, Mathematics - Symplectic Geometry, Supermanifolds and graded manifolds, FOS: Mathematics, symplectic manifolds, Symplectic Geometry (math.SG), compactness, removal of singularities, Gromov topology, Implicit function theorems; global Newton methods on manifolds
Global theory of symplectic and contact manifolds, holomorphic curves, Mathematics - Symplectic Geometry, Supermanifolds and graded manifolds, FOS: Mathematics, symplectic manifolds, Symplectic Geometry (math.SG), compactness, removal of singularities, Gromov topology, Implicit function theorems; global Newton methods on manifolds
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