Complex symplectic structures: deformations and cohomology
Giovanni Bazzoni, Marco Freibert, Adela Latorre, and Nicoletta Tardini
TL;DR
This paper investigates how complex symplectic structures behave under small deformations, identifying conditions for their preservation and exploring cohomological obstructions to their existence.
Contribution
It provides new insights into the deformation stability of complex symplectic structures and analyzes cohomological conditions affecting their existence.
Findings
Complex symplectic structures may not be preserved under small deformations.
Sufficient conditions for preservation are identified.
Topological obstructions to the existence of such structures are studied.
Abstract
We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of compact complex symplectic manifolds, obtaining some topological obstructions to their existence.
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