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


Syllabus
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. Blow-ups.
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.