Automorphism Groups of Generic Hyperkähler Manifolds - a Note Inspired by Curtis T. Mcmullen

Bimeromorphic Automorphism Groups of Non-projective Hyperkähler Manifolds - a Note Inspired by C. T. Mcmullen

Being inspired by a work of Curtis T. McMullen about a very impressive automorphism of a K3 surface of Picard number zero, we shall clarify the structure of the bimeromorphic automorphism group of a non-projective hyperkähler manifold, up to finite group factor. We also discuss relevant topics, especially, new counterexamples of Kodaira’s problem about algebraic approximation of a compact Kähle...

Groups of Automorphisms of Null-entropy of Hyperkähler Manifolds

The following two results are proven: The full automorphism group of any non-projective hyperkähler manifold M is almost abelian of rank at most maximum of ρ(M) − 1 and 1. Any groups of automorphisms of nullentropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. A few applications for K3 surfaces are also given.

Horocycles in hyperbolic 3-manifolds

Knots which Behave Like the Prime Numbers

This paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.

Automorphism Groups and Anti-pluricanonical Curves

We show the existence of an anti-pluricanonical curve on every smooth projective rational surface X which has an infinite group G of automorphisms of either null entropy or of type Z⋉Z, provided that the pair (X,G) is minimal. This was conjectured by Curtis T. McMullen (2005) and further traced back to Marat Gizatullin and Brian Harbourne (1987). We also prove (perhaps) the strongest form of th...