Konfiguracije 9 točk na kubični krivulji : delo diplomskega seminarja

Fajfar, Matija (author), Šivic, Klemen (mentor)

Raziščemo incidenčne strukture devetih točk v projektivni ravnini. Posebej nas zanimajo strukture, ki ležijo na nerazcepni kubični krivulji. Te klasificiramo glede na nivo strukture in polje, v katerem ležijo. Pod določenimi pogoji najdemo 162 incidenčnih struktur, od teh je 158 struktur realizabilnih v nekem ambientnem prostoru, 133 od teh pa lahko leži na nerazcepni kubiki. Hilbertova funkcija ideala točk struktur lahko zavzame eno od le dveh oblik.

• Language: Slovenian
• Keywords: incidenčna struktura, kubika, konfiguracija, Hilbertova funkcija
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-162404
• UDC: 515.1
• COBISS.SI-ID: 208574723
• Publication date in RUL: 22.09.2024

Secondary language

• Language: English
• Title: On the configurations of 9 points on a cubic curve

Abstract

We explore incidence structures of nine points in the projective plane, particularly those contained in an irreducible cubic curve. We classify these according to the level of the structure and the field within which they exist. Under certain conditions we find 162 incidence structures, of those 158 are realizable over some ambient space, 133 of those structures may lie on an irreducible cubic. The Hilbert function of the ideal of points of the structure can take one of only two possible forms.

• Keywords: incidence structure, cubic, configuration, Hilbert function