Authors compute ring structure, coherent cohomology (via Lie algebra reduction), Poincaré duality compatibility, and Picard groups for supertori defined by odd-parameter translations in superspace.
Manin.Gauge Field Theory and Complex Geometry
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Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.
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Cohomology of complex supertori
Authors compute ring structure, coherent cohomology (via Lie algebra reduction), Poincaré duality compatibility, and Picard groups for supertori defined by odd-parameter translations in superspace.
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Noncommutative differential geometry of ambiskew polynomial rings
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.