On the regularity of geodesic rays associated to test configurations

Abstract

Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation. Geometrically, this is accomplished by the use a positive line bundle on the resolution which is trivial outside of the exceptional divisor.

References in corpus (5)

• The Space of Kähler metrics (II)
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Infinite geodesic rays in the space of Kahler potentials
• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance

Cited by in corpus (2)

• Orthogonal projection of a test configuration to vector fields
• Note on geodesic rays tamed by simple test configurations