Language: English
Teaching style: In presence
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.
MATTEO PENEGINI (President)
MAURO CARLO BELTRAMETTI
STEFANO VIGNI
February 27, 2017
BASICS OF HIGHER GEOMETRY 2
