On the rank of general linear series on stable curves

verfasst von

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.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Externe Organisation(en)

Ben-Gurion University of the Negev (BGU)

Typ

Artikel

Journal

Mathematische Annalen

Band

388

Seiten

2217–2240

Anzahl der Seiten

24

ISSN

0025-5831

Publikationsdatum

02.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2005.12817 (Zugang: Offen)
https://doi.org/10.1007/s00208-023-02576-z (Zugang: Offen)