96733 - Algebraic Curves and Surfaces

Learning outcomes

The goal of the course is to provide a robust introduction to techniques, problems and applications in algebraic geometry.

Course contents

Introduction to affine and projetice curves and surfaces, as abstract algebraic varieties and their properties.

Ideals, varieties, ring of functions, field of functions. Examples. Maps, Morphisms. Abstract varieties. Weighted projective spaces and other examples. Singular and non singular varities. Dimensions. Quotients.  Volume forms. The canonical divisor. Adjunction formula. Divisors, linear systems.  Examples and applications. Birationality problems; Rationality questions.

The courses Curves and Surfaces  and Projective Geometry can be taken in the same year or in different years, in any sequence. The courses do not overlap, rather, they complement each other; the syllabi wiil be coordinated.

 

Readings/Bibliography

M. Reid, Undergraduate Algebraic Geometry

A. Grassi, Appunti del corso

Other materials and papers posted on  Virtuale

Teaching methods

Blackboards  and digital presentations.

Assessment methods

 

Oral exam.

Office hours

See the website of Antonella Grassi