Reading Course on Algebraic Surfaces, Fall 2018

Organizer: Yuchen Liu

Office: LOM 219B

Office hours: by appointments


Main textbook: Complex Algebraic Surfaces, 2nd edition, Arnaud Beauville, Cambridge University Press.

Algebraic Geometry Chapter V, Robin Hartshorne, Springer.

Compact Complex Surfaces, 2nd enlarged edition, W. Barth, K. Hulek, C. Peters, and A. van de Ven, Springer.

Lecture notes by Ravi Vakil.


We meet for Lectures on Wednesdays from 10:30am to 12pm.

Wed Sep. 5: First meeting, intersection of curves on surfaces

Wed Sep. 12: Riemann-Roch theorem, blow-ups

Thu Sep. 20 (2-3:30pm): Rational maps, elimination of indeterminancy

Wed Oct. 3: Decomposition of birational maps, Castelnuovo's contractibility criterion

Wed Oct. 10: Ruled surfaces, Noether-Enriques theorem

Fri Oct. 26 (8:30-10am): Minimal ruled surfaces, Grothendieck splitting theorem

Wed Oct. 31: Ruled surfaces over elliptic curves, numerical invariants of ruled surfaces

Wed Nov. 28: MMP for surfaces

Wed Dec. 5: Abundance for surfaces of general type

Fri Dec. 14 (10:30-12pm): Introduction to K3 surfaces