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