A note on the K\"ahler and Mori cones of hyperk\"ahler manifolds
Giovanni Mongardi
TL;DR
This paper investigates the geometric structure of hyperk"ahler manifolds, showing that their K"ahler and Mori cones are characterized by divisors meeting specific numerical criteria.
Contribution
It establishes a link between the walls of the K"ahler cone and extremal rays of the Mori cone through divisors with particular numerical properties.
Findings
Walls of the K"ahler cone are determined by certain divisors.
Extremal rays of the Mori cone are characterized by divisors with specific numerical conditions.
The results provide a unified description of cone structures in hyperk"ahler geometry.
Abstract
In the present paper we prove that, on a hyperk\"ahler manifold, walls of the k\"ahler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.
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