Continuous Linear Series
Algebraic Geometry
2025-10-14 v1
Abstract
We parameterize by a fine moduli space all degenerations of linear series to a singular curve which is the union of two smooth components meeting transversally at a single point. For this we introduce a novel object in the study of degenerations of linear series, which is the continuous linear series. Our moduli space can be regarded as a Hilbert quotient, in the terminology introduced by Kapranov, and is a new compactification of Osserman moduli space of exact limit linear series, and consequently, of Eisenbud and Harris moduli space of refined limit linear series on the curve.
Keywords
Cite
@article{arxiv.2510.11623,
title = {Continuous Linear Series},
author = {Eduardo Esteves and Antonio Nigro and Pedro Rizzo},
journal= {arXiv preprint arXiv:2510.11623},
year = {2025}
}