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INTRODUCTION TO ALGEBRAIC GEOMETRY

CODE 61707
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/03
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    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

    MATTEO PENEGINI (President)

    VICTOR LOZOVANU

    ARVID PEREGO (President Substitute)

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    EXAMS

    EXAM DESCRIPTION

    Oral.