## Reading Course on Algebraic Surfaces, Fall 2018

**Organizer**: Yuchen Liu

Office: LOM 219B

Office hours: by appointments

## References

**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.

## Schedule

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