BASIC PROJECTIVE ALGEBRAIC GEOMETRY

BASIC PROJECTIVE ALGEBRAIC GEOMETRY

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iten
Code
66453
ACADEMIC YEAR
2019/2020
CREDITS
7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
MAT/03
TEACHING LOCATION
GENOVA (Mathematics)
semester
2° Semester
Teaching materials

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)

ARVID PEREGO

MATTEO PENEGINI

LESSONS

Teaching methods

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

BASIC PROJECTIVE ALGEBRAIC GEOMETRY

EXAMS

Exam description

Oral.