Dokument: On regular but non-smooth integral curves

Titel:	On regular but non-smooth integral curves
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=68069
URN (NBN):	urn:nbn:de:hbz:061-20250108-134908-9
Kollektion:	Publikationen
Sprache:	Englisch
Dokumententyp:	Wissenschaftliche Texte » Artikel, Aufsatz
Medientyp:	Text
Autoren:	Hilario, Cesar [Autor] Stöhr, Karl-Otto [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 513,5 KB in einer Datei [ZIP-Datei erzeugen] Dateien vom 08.01.2025 / geändert 08.01.2025
Stichwörter:	Non-conservative functions fields, Fibrations by singular curves, imperfect fields, Bertini’s theorem, Regular but non-smooth curves over
Beschreibung:	Let C be a regular geometrically integral curve over an imperfect field K and assume that it admits a non-smooth point which — seen as a prime of the separable function field — is non-decomposed in the base field extension . In this paper we establish a bound for the number of iterated Frobenius pullbacks needed in order to transform into a rational point. This provides an algorithm to compute geometric δ-invariants of non-smooth points and a procedure to construct fibrations with moving singularities of prescribed δ-invariants. We show that the bound is sharp in characteristic 2. We further study the geometry of a pencil of plane projective rational quartics in characteristic 2 whose generic fibre attains our bound. On our way, we prove several results on separable and non-decomposed points that might be of independent interest.
Rechtliche Vermerke:	Originalveröffentlichung: Hilario, C., & Stöhr, K.-O. (2024). On regular but non-smooth integral curves. Journal of Algebra, 661, 278–300. https://doi.org/10.1016/j.jalgebra.2024.08.002
Lizenz:	Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät
Dokument erstellt am:	08.01.2025
Dateien geändert am:	08.01.2025