BARTH'S SEXTIC                                 UBIQUITY OF ALGEBRAIC GEOMETRY                                     BLOW UP OF A PLANE   

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ALGEBRAIC GEOMETRY 1
Undergraduate and graduate studies in Mathematics
Roma Tre University
A.Y. 2014/2015 
                  

Teacher: Angelo Felice Lopez

SCHEDULE OF LESSONS:
Tuesday and Friday 2PM-4PM, room 009.

DIARY OF LESSONS

DESCRIPTION OF THE COURSE


Algebraic Geometry is the study of algebraic varieties, that is sets of common zeros of some polynomials. Historically this study is performed by the analysis of geometrical, algebraic, topological, differential, analytic and numerical properties. Such richness of points of view makes Algebraic Geometry one of the most fascinating and central areas of mathematics. Many famous problems in mathematics, like Fermat's Last Theorem, have been solved with the essential use of Algebraic Geometry.
The course introduces to basic properties of
affine and projective algebraic varieties, to maps among them, to their local geometry and to the theory of divisors and linear systems.

OUTLINE OF CONTENT

Classical theory of
algebraic varieties, affine and projective, over algebraically closed fields. Local geometry, normalization. Divisors, linear systems and associated morfisms (time permetting).

SUGGESTED BOOKS:

We will follow closely the lecture notes written by L. Caporaso (the notes will be given in class).

We also suggest the following classical textbooks:

*
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, 1977.
* J. Harris, Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer-Verlag, New York-Heidelberg, 1977.

and

Commutative Algebra textbooks:

* M. Artin, Algebra, Pearson Education 2014.
* M.F. Atiyah, I.G. Mac Donald, Introduction to commutative algebra,
Sarat Book House, 1996.