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math.AG2026
A birational version of K-stability for big classes
Ruadhaí Dervan, Rémi Reboulet
We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and f…
math.AG2024
Arcs, stability of pairs and the Mabuchi functional
Ruadhaí Dervan, Rémi Reboulet
We prove various results involving arcs - which generalise test configurations - within the theory of K-stability. Our main result characterises coercivity of the Mabuchi functiona…
math.AG2019
K-semistability of optimal degenerations
Ruadhaí Dervan
K-polystability of a polarised variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature Kähler metric. When a variety is K-un…