Automorphisms and examples of compact non K\"ahler manifolds
Gunnar \TH\'or Magn\'usson

TL;DR
This paper explores the properties of automorphisms on certain compact K"ahler manifolds and uses these insights to construct examples of compact non-K"ahler manifolds that challenge existing conjectures in complex geometry.
Contribution
It introduces new examples of non-K"ahler manifolds by applying automorphism properties, providing counterexamples to the abundance and Iitaka conjectures.
Findings
Automorphisms of certain K"ahler manifolds have finite order.
Constructed non-K"ahler manifolds contradict key conjectures.
Automorphism constraints lead to new manifold examples.
Abstract
If is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of is finite. We apply this well known result to construct compact non-K\"ahler manifolds. These manifolds contradict the abundance and Iitaka conjectures for complex manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows
