Extension of 2-forms and symplectic varieties
Yoshinori Namikawa

TL;DR
This paper explores symplectic varieties lacking symplectic resolutions, including moduli spaces on K3 surfaces and symplectic V-manifolds, proving a local Torelli theorem and discussing symplectic singularities.
Contribution
It extends the theory of 2-forms to symplectic varieties without resolutions and proves a local Torelli theorem for these complex structures.
Findings
Proved local Torelli theorem for certain symplectic varieties
Analyzed properties of symplectic singularities
Studied moduli spaces of sheaves on K3 surfaces
Abstract
This paper deals with symplectic varieties which do not have symplectic resolutions. Some moduli spaces of semi-stable torsion-free sheaves on a K3 surface, and symplectic V-manifolds are such varieties. We shall prove local Torelli theorem for symplectic varieties. Some results on symplectic singularities are also included.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometry and complex manifolds
