On the rank of general linear series on stable curves

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Karl Christ

Research Organisations

External Research Organisations

  • Ben-Gurion University of the Negev
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Details

Original languageEnglish
Pages (from-to)2217–2240
Number of pages24
JournalMathematische Annalen
Volume388
Issue number2
Early online date7 Feb 2023
Publication statusPublished - Feb 2024

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.

Keywords

    math.AG, 14H20, 14H40, 14H51

ASJC Scopus subject areas

Cite this

On the rank of general linear series on stable curves. / Christ, Karl.
In: Mathematische Annalen, Vol. 388, No. 2, 02.2024, p. 2217–2240.

Research output: Contribution to journal › Article › Research › peer review

Christ K. On the rank of general linear series on stable curves. Mathematische Annalen. 2024 Feb;388(2):2217–2240. Epub 2023 Feb 7. doi: 10.48550/arXiv.2005.12817, 10.1007/s00208-023-02576-z
Christ, Karl. / On the rank of general linear series on stable curves. In: Mathematische Annalen. 2024 ; Vol. 388, No. 2. pp. 2217–2240.
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