Topics in Holomorphic Symplectic and Hyperkahler Geometry

Research project

Description

The P.I.'s recent work has spanned a number of different areas: complex algebraic and analytic geometry, differential geometry, and arithmetic geometry. He has studied Lagrangian fibrations on holomorphic symplectic manifolds, proving a finiteness theorem and classifying fibrations by Jacobians. He has developed Kummer-type constructions leading to new examples of holomorphic symplectic orbifolds. He has studied generalized complex structures (in the sense of Hitchin) on K3 surfaces and hyperkahler manifolds, and proved the existence of a generalized twistor space. He has used Brauer elements on K3 surfaces over number fields to find obstructions to the existence of rational points. The P.I. will use the collaboration grant to continue with these projects, and other projects on which he is currently working.
StatusActive
Effective start/end date9/1/158/31/20

Funding

  • Simons Foundation

Fingerprint

K3 Surfaces
Fibration
Co-ordinate geometry
Twistor Space
Symplectic Manifold
Algebraic Geometry
Rational Points
Complex Geometry
Orbifold
Differential Geometry
Finiteness
Obstruction
Complex Structure
Number field
Continue
Theorem
Collaboration