BASICS OF HIGHER GEOMETRY 2
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.
EXAMS
Exam description
Oral.