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## BASIC PROJECTIVE ALGEBRAIC GEOMETRY

CODE 66453 2018/2019 7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA 7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA MAT/03 GENOVA (Mathematics) 2° Semester AULAWEB

## OVERVIEW

Language: Italian

## AIMS AND CONTENT

### LEARNING OUTCOMES

The aim of the course is to provide an introduction to the theory of algebraic varieties, with the study of remarkable examples and with particular regard to the case of the curves, by dealing with classical methods also some advanced topics. The knowledge provided is useful both for the continuation of studies in the algebraic-geometric field and for an approach to some problems in the field of application.

### TEACHING METHODS

Teaching style: In presence

### SYLLABUS/CONTENT

Affine and projective algebraic sets. Non-singular points and  tangent space. Dimension and degree of a projective variety. Hypersurfaces in projective space. Linear systems of hypersurfaces. The Jacobian group of a linear system on a line. Algebraic correspondences between lines. Birational plane model of a projective curve. Plane curves. Cusps, flexes and ordinary multiple points. Bézout’s  theorem. The genus of a plane curve (according to Riemann). Rational curves. Rational normal curves. Elliptic normal curves. Plane cubic curves. Modulus  of a plane cubic. Structure of abelian group  on such curves. Modulus  of a plane cubic. Classification of degree 3 projective curves.

## TEACHERS AND EXAM BOARD

### Exam Board

STEFANO VIGNI (President)

MAURO CARLO BELTRAMETTI

ARVID PEREGO

## LESSONS

### TEACHING METHODS

Teaching style: In presence

### LESSONS START

The class will start according to the academic calendar.

### Class schedule

BASIC PROJECTIVE ALGEBRAIC GEOMETRY

Oral.