The Moser isotopy for holomorphic symplectic and Csymplectic structures
Abstract
A Csymplectic structure is a complexvalued 2form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of Csymplectic structures and list several applications of this result. We prove that the degenerate twistorial deformation associated to a holomorphic Lagrangian fibration is locally trivial over the base of this fibration. This is used to extend several theorems about Lagrangian fibrations, known for projective hyperkähler manifolds, to the nonprojective case. We also exhibit new examples of noncompact complex manifolds with infinitely many pairwise nonbirational algebraic compactifications.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 DOI:
 10.48550/arXiv.2109.00935
 arXiv:
 arXiv:2109.00935
 Bibcode:
 2021arXiv210900935S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 Updated references