2014/10/12 by Michael Temkin, Temkin, Michael · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1410.3079
openalex publication_date 2014/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a general notion of a seminorm on sheaves of rings or modules and provide each sheaf of relative differential pluriforms on a Berkovich k-analytic space with a natural seminorm, called Kahler seminorm. If the residue field is of characteristic zero and X is a quasi-smooth k-analytic space, then we show that the maximality locus of any global pluricanonical form is a PL subspace of X contained in the skeleton of any semistable formal model of X. This extends a result of Mustata and Nicaise, because the Kahler seminorm on pluricanonical forms coincides with the weight norm defined by Mustata and Nicaise when k is discretely valued and of residue characteristic zero.