Generalities

January Lectures Schedule - prof. D. Lewanski:

9/1/2023 14:00 - 17:00 room 4B  H2bis, UNITS

Textbooks:

I.R. Shafarevich: Basic Algebraic Geometry 1: Varieties in Projective Space,Third edition. Springer, Heidelberg, 2013

J. Harris: Algebraic geometry. A first course, Graduate Texts in Mathematics, 133, Springer-Verlag, New York, 1995. 

R. Hartshorne: Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977. (first chapter)

E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, 1985

M.F. Atiyah - I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969 

Lothar Goettsche: Introduction to Algebraic Geometry

 https://users.ictp.it/~gottsche/algcourse.ps

Main topics of the course:

Algebraic geometry of affine and projective varieties. 

Zariski topology on affine and projective varieties. Hilbert Nullstellensatz. Regular and rational maps. Tangent spaces and singular points. Blow-up and outline of the resolution of singularities for curves. Grassmannians.

Goals:

KNOWLEDGE AND UNDERSTANDING

By the end of the course the student is expected to be familiar with the fundamental objects of classical algebraic geometry, both affine and projective, and of basic concepts of commutative algebra.

CAPACITY TO APPLY KNOWLEDGE AND UNDERSTANDING

By the end of the course the student is expected to be able to apply the notions of basic algebraic geometry acquired to solve problems and exercises of medium difficulty. The exercises can also be proposed as easy theoretical results.

JUDGMENT AUTONOMY

By the end of the course the student is expected to be able to recognize and apply the most basic techniques of algebraic geometry and also to recognize the situations and problems in which these techniques can be used advantageously.

COMMUNICATIVE SKILLS

By the end of the course the student is expected to be able to express himself with proficient command of language and exposure security on the topics of the course.

LEARNING CAPACITY

By the end of the course the student is expected to be able to consult the standard texts of algebraic geometry and commutative algebra.

Required background:

Linear algebra, affine and projective space and their subspaces; basic notions of general topology; a basic knowledge of plane algebraic curves is useful but not essential.

Information on the exam:

The exam program coincides with the arguments of the lectures. During the lectures there will some exercise assignments, to be presented during the course.

The exam will be held in oral form only, but the students who don't present the assigned exercises will have to solve some exercises similar to the assigned ones.

 The oral exam aims to carry out an assessment of the student’s familiarity with the program, comprehension of the contents (definitions and proofs) and command of language.

WINTER EXAM SESSION:

16/01/2023, 10:00 Room 5B, H2 bis

For additional dates, write to beorchia@units.it

If the esse3 system does not allow you to register, please write to beorchia@units.it