
ALGEBRAIC GEOMETRY 2
Second cycle degree in MATHEMATICS
Campus:
PADOVA
Language:
English
Teaching period:
Second Semester
Lecturer:
CARLA NOVELLI
Number of ECTS credits allocated:
6
Prerequisites:

Basics on topology and commutative algebra. 
Examination methods:

Seminar. 
Course unit contents:

Introduction to affine and projective varieties.
Morphisms, rational maps and birational maps.
Singularities and resolution of singularities. Blowups.
Introduction to sheaves and cohomology.
Rational curves and divisors on varieties.
Ampleness and cones of curves.
Extremal rays and extremal contractions.
Surfaces: Cone Theorem, birational classification and Minimal Model Program.
Higher dimensional varieties: Cone Theorem, Contraction Theorem, Extremal Rays, contractions associated with extremal rays, introduction to Minimal Model Program and Minimal Models. 

