Original title: Rezolventy singularit pomocí blow-upů
Translated title: Resolutions of singularities using blow-ups
Authors: Komora, Matúš ; Šťovíček, Jan (advisor) ; Hrbek, Michal (referee)
Document type: Bachelor's theses
Year: 2023
Language: eng
Abstract: [eng] [cze]
This bachelor's thesis aims to provide accessible treatment of the blow-up construction for algebraic varieties. The blow-up construction is a fundamen- tal technique in algebraic geometry that allows us to find a variety which has better properties than an original variety but is still equivalent to the original. This process can be used to resolve singularities. In the first two chapters, we begin by providing an introduction to the fundamental principles of alge- braic geometry, including the definitions of algebraic varieties but also basic topological concepts but also some construction such as Segre embedding and product of varieties. In the third chapter, we will introduce the concept of blow-ups and show the computation as on example. 1 Táto bakalárska práca sa zameriava na jednoduchý úvod do blow-upov algebraických variet. Konštrukcia blow-upov je jednou zo základných techník v algebraickej geometrii, ktorá nám umožňuje nájsť varietu, ktorá má lepšie vlastnosti ako pôvodná varieta, ale stále je ekvivalentná pôvodnej. Tento proces môžeme použiť na rozriešenie singularít. V prvých dvoch kapitolách začneme poskytnutím úvodu do základných princípov algebraickej geometrie, vrátane definícií algebraických variet a základných topologických pojmov, ale, aj niektorých konštrukcií, ako je napríklad Segreho vnorenie a súčin variet. V tretej kapitole predstavíme konštrukciu blow-upov a ukážeme ju na príklade. 1
Keywords: blow-up|singularity|resolution|algebraic geometry; blow-up|algebraicka geometrie|singularity

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/179252

Permalink: http://www.nusl.cz/ntk/nusl-521062


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses