Holomorfni avtomorfizmi : delo diplomskega seminarja

Horjak, Luka (author), Černe, Miran (mentor)

Na mnogih matematičnih področjih so glavna tema preslikave z določenimi lastnostmi -- homomorfizmi, homeomorfizmi, ali pa kar poljubne preslikave med množicami. Posebej zanimive so bijektivne preslikave, ki imajo za domeno in kodomeno isti objekt in jim pravimo avtomorfizmi tega objekta. Te nam namreč opišejo simetrije nekega objekta. V kompleksni analizi imamo tako opravka s holomorfnimi avtomorfizmi, ki ohranjajo kote. Cilj diplomskega dela je analiza grup holomorfnih avtomorfizmov nekaterih območij v kompleksni ravnini in kompaktnih Riemannovih ploskev.

• Language: Slovenian
• Keywords: holomorfen avtomorfizem, Riemannova ploskev, divizor
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-150733
• UDC: 517.5
• COBISS.SI-ID: 165458691
• Publication date in RUL: 22.09.2023

Secondary language

• Language: English
• Title: Holomorphic automorphisms

Abstract

The main theme of many mathematical subjects are maps with some properties -- be it homomorphisms, homeomorphisms, or just any map between sets. Especially interesting are bijective maps with the same object as domain and codomain, which are called automorphisms of said object. These describe symmetries of the object. In complex analysis, we deal with holomorphic automorphisms, which preserve angles. The goal of this thesis is to analyze groups of holomorphic automorphisms of some domains in the complex plane and of compact Riemann surfaces.

• Keywords: holomorphic automorphism, Riemann surface, divisor