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http://hdl.handle.net/2445/198705
Title: | Introduction to complex geometry and Calabi-Yau manifolds motivated by physics |
Author: | Lladó Duran, Marc |
Director/Tutor: | Cirici, Joana |
Keywords: | Àlgebra homològica Treballs de fi de grau Geometria algebraica Varietats de Calabi-Yau Geometria diferencial Homological algebra Bachelor's theses Algebraic geometry Calabi-Yau manifolds Differential geometry |
Issue Date: | 24-Jan-2023 |
Abstract: | [en] In this work, we give an introduction to complex geometry and Calabi-Yau manifolds. We begin by recalling the necessary background of differential geometry, as well as defining the de Rahm cohomology and the Ricci curvature. Then we turn to complex geometry, giving some precise examples, extending differential forms to the complex case and defining Dolbeault cohomology, Chern classes and holonomy. We then focus on Kähler manifolds, which are the previous steps to define Calabi-Yau manifolds, whose properties will be briefly studied. We close the work with a few ideas of a basic string theory model. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Joana Cirici |
URI: | http://hdl.handle.net/2445/198705 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_llado_duran_marc.pdf | Memòria | 489.45 kB | Adobe PDF | View/Open |
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