4 papers
Extremal metrics on the total space of destabilising test configurations
Lars Martin Sektnan, Cristiano Spotti
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples o…
Uniqueness of optimal symplectic connections
Ruadhaí Dervan, Lars Martin Sektnan
Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constant scalar curvature Kähler metric. When the fibres admit continuous automorp…
Blowing up extremal Poincaré type manifolds
Lars Martin Sektnan
We prove a version of the Arezzo-Pacard-Singer blow-up theorem in the setting of Poincaré type metrics. We apply this to give new examples of extremal Poincaré type metrics. A key…
Extremal Kähler Poincaré type metrics on toric varieties
Vestislav Apostolov, Hugues Auvray, Lars Martin Sektnan
We develop a general theory for the existence of extremal Kähler metrics of Poincaré type in the sense of Auvray, defined on the complement of a toric divisor of a polarized toric…