On the rank of general linear series on stable curves

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Karl Christ

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Externe Organisationen

  • Ben-Gurion University of the Negev (BGU)
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Details

OriginalspracheEnglisch
Seiten (von - bis)2217–2240
Seitenumfang24
FachzeitschriftMathematische Annalen
Jahrgang388
Ausgabenummer2
Frühes Online-Datum7 Feb. 2023
PublikationsstatusVeröffentlicht - 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.

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On the rank of general linear series on stable curves. / Christ, Karl.
in: Mathematische Annalen, Jahrgang 388, Nr. 2, 02.2024, S. 2217–2240.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 ; Jahrgang 388, Nr. 2. S. 2217–2240.
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