PhD Course: Cones of divisors and positivity
A first course in Birational Geometry
Spring 2019
Course description:
- Ample and nef divisors
- The ample and nef cones. The cone of effective curves and duality
- Cone Theorem (smooth case). MMP in dimension 2
- Kodaira dimension
- Big divisors. Kawamata-Viehweg vanishing theorem
- Volume of big divisors
- The cones of big and pseudoeffective divisors
- Boucksom-Demailly-Peternell-Paun Theorem
Meetings:
- January 28th, 2-4pm, Aula Tricerri
- January 30th, 12:30-2:30pm, Aula Tricerri
- February 11th, 2-4pm, Aula Tricerri
- February 13th, 12:30-2:30pm, Aula Tricerri
- February 19th, 2-4pm, Aula Tricerri
- February 25th, 2-4pm, Aula Tricerri
- February 28th, 2-4pm, Aula Tricerri
References:
- R. Lazarsfeld “Positivity in Algebraic Geometry I and II”
Springer, 2004
- J. Kollár and S. Mori “Birational Geometry of Algebraic Varieties”
Cambridge University Press, 1998
- O. Debarre “Hidger-Dimensional Algebraic Geometry”
Springer Universitext, 2001