Year: 2026
Type: preprint
Abstract: We introduce relative versions of non-nef loci and restricted base loci, and investigate a relative version of Boucksom--Broustet--Pacienza's conjecture that these two loci coincide. We prove the conjecture holds for normal integral schemes projective and flat over a Dedekind domain of characteristic zero with mild singularities, such as BCM-regularity. This result is a mixed characteristic analogue of results of Cacciola--Di Biagio in characteristic zero and Sato in positive characteristic. To prove this result, we show that BCM-regularity is preserved under perturbations by divisors with small vanishing order.
Source: arXiv (Cornell University)
Author: Iwane, Ryotaro
Institution: The University of Tokyo
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207563950
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