Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces.
teacher profile teaching materials
- Local geometry, normalization.
- Divisors, linear systems and morphisms of projective varieties.
R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977.
I. Shafarevich, Basic algebraic geometry vol. 1, Springer-Verlag, New York-Heidelberg, 1994.
J. Harris, Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer-Verlag, New York-Heidelberg, 1992.
Algebra texts:
* M. Artin, Algebra, Bollati Boringhieri 1997.
* M.F. Atiyah, I.G. Mac Donald, Introduzione all'algebra commutativa, Feltrinelli 1991.
Mutuazione: 20402104 GE410 - GEOMETRIA ALGEBRICA 1 in Matematica LM-40 N0 MASCARENHAS MELO ANA MARGARIDA
Programme
- Classical theory of algebraic varieties in affine spaces over algebraically closed fields.- Local geometry, normalization.
- Divisors, linear systems and morphisms of projective varieties.
Core Documentation
Algebraic Geometry texts:R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977.
I. Shafarevich, Basic algebraic geometry vol. 1, Springer-Verlag, New York-Heidelberg, 1994.
J. Harris, Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer-Verlag, New York-Heidelberg, 1992.
Algebra texts:
* M. Artin, Algebra, Bollati Boringhieri 1997.
* M.F. Atiyah, I.G. Mac Donald, Introduzione all'algebra commutativa, Feltrinelli 1991.
Type of delivery of the course
frontal lecturesType of evaluation
Exercises and a seminar talk.