First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC02120637, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ALGEBRAIC GEOMETRY 2
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge CARLA NOVELLI MAT/03

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/03 Geometry 6.0

Mode of delivery (when and how)
Period Second semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Start of activities 26/02/2018
End of activities 01/06/2018

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 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.
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)
  • Arnaud Beauville, Complex Algebraic Surfaces (Second Edition). London Mathematical Society.: Cambridge: Cambridge University Press, 1996. Student Text 34 Cerca nel catalogo
  • Olivier Debarre, Higher-Dimensional Algebraic Geometry. New York: Universitext, Springer-Verlag, 2001. Cerca nel catalogo
  • Ja'nos Kolla'r & Shigefumi Mori, Birational Geometry of Algebraic Varieties. Cambridge: Cambridge University Press, 1998. Cambridge Tracts in Mathematics 134 Cerca nel catalogo
  • Kenji Matsuki, Introduction to the Mori Program. New York: Universitext, Springer-Verlag, 2002. Cerca nel catalogo