CODE 61707 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 1 MATEMATICA 9011 (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 ARVID PEREGO MATTEO PENEGINI Exam Board MATTEO PENEGINI (President) VICTOR LOZOVANU ARVID PEREGO (President Substitute) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule INTRODUCTION TO ALGEBRAIC GEOMETRY EXAMS EXAM DESCRIPTION Oral.
