BASICS OF HIGHER GEOMETRY 2

BASICS OF HIGHER GEOMETRY 2

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iten
Code
61707
ACADEMIC YEAR
2018/2019
CREDITS
8 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/03
LANGUAGE
Italian (English on demand)
TEACHING LOCATION
GENOVA (Mathematics)
semester
1° Semester
Teaching materials

OVERVIEW

Language: English

AIMS AND CONTENT

LEARNING OUTCOMES

The course objective is to present an elemental introduction to the concepts and methods of Modern Algebraic Geometry.

Teaching methods

Teaching style: In presence

SYLLABUS/CONTENT

Affine algebraic sets and affine varieties. Irreducible components. Hilbert Nullstellensatz. Regular and rational functions on an affine algebraic variety. Regular and rational maps between two affine varieties. Examples. Projective algebraic varieties and projective Nullstellensatz. Rational functions on a projective variety. Regular and rational maps between two projective varieties. Examples of projective varieties. Sheaves in algebraic geometry, (quasi‐)coherent sheaves. Definitions of schemes. The Picard variety. The tangent space at an algebraic variety in a point. The Zariski cotangent space. General properties. Singular and nonsingular points. Divisors on a projective nonsingular curve. The formulation of Riemann‐Roch for curves. Examples.

TEACHERS AND EXAM BOARD

Exam Board

ARVID PEREGO (President)

ETTORE GIOVANNI CARLETTI

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:

BASICS OF HIGHER GEOMETRY 2

EXAMS

Exam description

Oral.