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Last updated:

November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

The main aims of this seminar will be to go over

the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Course Curriculum

  • Introduction Unlimited
  • Linear equivalence, algebraic equivalence, numerical equivalence of divisors Unlimited
  • Birational maps, rational maps, linear systems, properties of birational maps between surfaces Unlimited
  • Birational maps (cont.) Unlimited
  • Ruled surfaces I Unlimited
  • Ruled surfaces II Unlimited
  • Ruled surfaces III, rational surfaces Unlimited
  • Linear systems, rational normal scrolls Unlimited
  • Castelnuovo’s criterion for rationality Unlimited
  • Picard variety Unlimited
  • Albanese variety Unlimited
  • Non-ruled and ruled surfaces Unlimited
  • Classification of ruled surfaces Unlimited
  • Elliptic and quasi-elliptic surfaces Unlimited
  • Elliptic surfaces (cont.), Kodaira dimension 0 Unlimited
  • K3 surfaces Unlimited
  • Enriques surfaces, bielliptic surfaces Unlimited
  • Classification Unlimited
  • Elliptic/quasi-elliptic fibrations I Unlimited
  • Elliptic/quasi-elliptic fibrations II Unlimited
  • Elliptic/quasi-elliptic fibrations III, classification Unlimited
  • Moduli Unlimited

About the instructor

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Massachusetts Institute of Technology