Geometry
Code
9642
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teaching language
Português
Objectives
The main goal is to introduce to the studentes the methods of Algebraic Geometry, namely, to give them the basic tools such that they will be able to work with the concepts of affine or projective varieties and their morphisms which it will be a start point for further research in this area.
Prerequisites
Linear Algebra: vector space, dimension, matrix, linear transformations
Algebra: field, ring, ideal, polynomial ring with coefficients in a field
Topology: open and closed topology, quotient topology
Subject matter
- Algebraic Varieties
- Theory of sheaves
- Application to the local analitic geometry
- Divisors
- Vector bundles on algebraic curves
Bibliography
- "Algebraic Geometry", Robin Hartshorne, Springer-Verlag, Graduate Texts in
Mathematics, 52, 1977. - "Introduction to Commutative Algebra", M.F. Atiyah, I.G. Macdonald, Westview Press (Perseus Books Group), 1969.
- "Local Analytic Geometry ", Thei de Jong, G. Pfister , Vieweg, 2000.
- "A singular introduction to Commutative Algebra", G.M.Greuel, G. Pfister, Springer-Verlag, 2002.
- "Algebraic Curves and Riemann surfaces", Rick Miranda, American Math. Soc., 199, 1995