On the rank of general linear series on stable curves

authored by: Karl Christ
Abstract: We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree \(d = g - 1\), we characterize when the effective locus gives a Theta divisor. In case of degree \(g - 2\) and \(g\), we show that the locus is either empty or has the expected dimension. This leads to a new characterization of semistability in these degrees. In the remaining cases, we show that the special locus has codimension at least \(2\). If the multidegree in addition is non-negative on each irreducible component of the curve, we show that the special locus contains an irrreducible component of expected dimension.
Organisation(s): Institute of Algebraic Geometry
External Organisation(s): Ben-Gurion University of the Negev
Type: Article
Journal: Mathematische Annalen
Volume: 388
Pages: 2217–2240
No. of pages: 24
ISSN: 0025-5831
Publication date: 02.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mathematics(all)
Electronic version(s): https://doi.org/10.48550/arXiv.2005.12817 (Access: Open)
https://doi.org/10.1007/s00208-023-02576-z (Access: Open)