Moduli problems in algebraic geometry

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Author(s):	Felipe César Freitas Monteiro Total Authors: 1
Document type:	Master's Dissertation
Press:	Campinas, SP.
Institution:	Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:	2022-02-15
Examining board members:	Marcos Benevenuto Jardim; Gaia Comaschi; Eduardo de Sequeira Esteves
Advisor:	Marcos Benevenuto Jardim
Abstract
The purpose of this dissertation is to study the abstract theory of moduli problems in Algebraic Geometry, describing David Mumford's Geometric Invariant Theory (or GIT) as a general framework for building moduli spaces in this context. We start by defining moduli problems and spaces using categorical language, with various examples, and then study GIT in chapters $2$ and $3$, over a field of characteristic zero. Afterwards, in the last chapter, we apply the developed tools to review the construction of the moduli space of (semi)stable vector bundles over smooth projective algebraic curves. We assume basic knowledge of scheme theory for most of the first three chapters, and in the fourth we also need to use tools from homological algebra and sheaf cohomology. The exposition follows the classical references for the subject, specially Prof. Victoria Hoskins' lecture notes (AU)

FAPESP's process:	19/20843-9 - Moduli problems in algebraic geometry
Grantee:	Felipe César Freitas Monteiro
Support Opportunities:	Scholarships in Brazil - Master