Construction of automorphisms of hyperk\"ahler manifolds
Ekaterina Amerik, Misha Verbitsky

TL;DR
The paper constructs deformations of hyperk"ahler manifolds with specific types of infinite order automorphisms, expanding understanding of their automorphism groups and geometric structures.
Contribution
It introduces methods to produce deformations of hyperk"ahler manifolds with hyperbolic and parabolic automorphisms of infinite order.
Findings
Existence of deformations with hyperbolic automorphisms for b2 ≥ 5.
Existence of deformations with parabolic automorphisms for b2 ≥ 14.
Automorphisms act hyperbolically on the space of real (1,1)-classes.
Abstract
Let be an irreducible holomorphic symplectic (hyperk\"ahler) manifold. If , we construct a deformation of which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its action on the space of real -classes is hyperbolic. If , similarly, we construct a deformation which admits a parabolic automorphism.
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.
