Year: 2025
Type: article
Abstract: We study the geometry of spaces of filtrations on a Noetherian local domain. We introduce a metric d 1 d_{1} on the space of saturated filtrations, inspired by the Darvas metric in complex geometry, such that it is a geodesic metric space. In the toric case, using Newton–Okounkov bodies, we identify the space of saturated monomial filtrations with a subspace of L loc 1 L^{1}_{\mathrm{loc}} . We also consider several other topologies on such spaces and study the semi-continuity of the log canonical threshold function in the spirit of Demailly–Kollár. Moreover, there is a natural lattice structure on the space of saturated filtrations, which is a generalization of the classical result that the ideals of a ring form a lattice.
Author: Lu Qi
Institutions: Princeton University, East China Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416181293