CODE 61707 ACADEMIC YEAR 2016/2017 CREDITS 8 cfu anno 1 MATEMATICA 9011 (LM-40) - 8 cfu anno 2 MATEMATICA 9011 (LM-40) - SCIENTIFIC DISCIPLINARY SECTOR MAT/03 LANGUAGE Italiano (Inglese a richiesta) TEACHING LOCATION SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW Language: English AIMS AND CONTENT 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 MATTEO PENEGINI STEFANO VIGNI Exam Board MATTEO PENEGINI (President) MAURO CARLO BELTRAMETTI STEFANO VIGNI LESSONS LESSONS START February 27, 2017 Class schedule BASICS OF HIGHER GEOMETRY 2 EXAMS Exam schedule Data appello Orario Luogo Degree type Note 05/06/2017 10:00 GENOVA Orale 23/06/2017 10:00 GENOVA Orale 12/07/2017 10:00 GENOVA Orale 04/09/2017 10:00 GENOVA Orale
