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ALGEBRAIC GEOMETRY 2 - 6 CFU

Teacher

Carla Novelli

Scheduled Period

I Year - 1 Semester | 30/09/2019 - 18/01/2020

Hours: 48 (24 esercitazione, 24 lezione)

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Prerequisites

Basics on topology and commutative algebra.

Target skills and knowledge

A good knowledge of the algebraic objects used in Birational Geometry.

Examination methods

Seminar.

Assessment criteria

The student will be evaluated on his/her understanding of the topics, on the acquisition of concepts and methodologies proposed and on the ability to apply them in full independence and awareness.

Course 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.

Planned learning activities and teaching methods

Lectures and recommended exercises.

Additional notes about suggested reading

Further material will be available in the moodle page of the course.

Textbooks (and optional supplementary readings)

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