2 citations · 2 across the 3 of their papers we have counts for
5 papers
Monge-Ampère measures on balanced polyhedral spaces
Ana María Botero, Enrica Mazzon, Léonard Pille-Schneider
We study classes of convex functions on balanced polyhedral spaces and establish various structural properties, including a compactness theorem for polyhedrally plurisubharmonic fu…
Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces
Léonard Pille-Schneider
Using a construction by Yamamoto of tropical contractions, we construct a non-archimedean SYZ fibration on the Berkovich analytification of a class of maximally degenerate hypersur…
Global pluripotential theory on hybrid spaces
Léonard Pille-Schneider
Let A be an integral Banach ring, and X/A be a projective scheme of finite type, endowed with a semi-ample line bundle L. We define a class PSH(X,L) of plurisubharmonic metrics on…
Toric geometry and integral affine structures in non-archimedean mirror symmetry
Enrica Mazzon, Léonard Pille-Schneider
We study integral dlt models of a proper C((t))-variety X along a toric stratum of the special fiber. We prove that the associated Berkovich retraction - from the non-archimedean a…
Hybrid convergence of Kähler-Einstein measures
Léonard Pille-Schneider
We compute the hybrid limit (in the sense of Boucksom-Jonsson) of the family of Kähler-Einstein volume forms on a degeneration of canonically polarized manifolds. The limit measure…