Plurisubharmonic geodesics in spaces of nonArchimedean metrics of finite energy
Abstract
Given a polarized projective variety (X,L) over any nonArchimedean field, assuming continuity of envelopes, we show that the space of finiteenergy metrics on L is a geodesic metric space, where geodesics are given as maximal psh segments. Given two continuous psh metrics, we show that the maximal segment joining them is furthermore continuous.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.07972
 arXiv:
 arXiv:2012.07972
 Bibcode:
 2020arXiv201207972R
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 Mathematics  Differential Geometry;
 32PO5;
 32U05;
 32U15;
 14G22
 EPrint:
 50 pages