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Instructional Workshop - Surfaces: Geometry and Arithmetic

Instructional Workshop - Surfaces: Geometry and Arithmetic

Monday 14th April - Friday 18th April 2008

 

This school is part of the April–June Active Period in Arithmetic Geometry and the 2007-2008 Warwick Maths Institute EPSRC Symposium.

Day 1:
  • Picard group and easy examples
  • Canonical divisor on hypersurface of degree d hypersurface in P^n (complete interscetions in exercises)
  • classification and the minimal model program
Day 2 and Day 3:
  • Picard group of del Pezzo surfaces, mentioning: Riemann-Roch on surfaces, genus and effectivity of (-1)-curves, the adjunction formula
  • Root lattices and their automorphism groups
  • Segre-Manin theorem for degree at least 4 (minus one for exercises) (S-M says existence of a rational point implies that rational points are Zariski-dense)
  • Segre-Manin for degree 3 del Pezzos
  • Growth of rational points of bounded height
Day 4 and Day 5 (Brauer-Manin obstruction):
  • explicitly computed examples of Brauer-Manin obstructions through quadratic reciprocity, the unenlightning way.
  • central simple algebras and Brauer groups
  • reformulate easy examples the enlightning way
  • harder Brauer-Manin obstruction examples (e.g. cubic surfaces) with given algebra
  • What was done to find the algebra?
  • Further directions. Brauer-Manin is not the only one, when is it?

Visit the Workshop Website for more information on this event.

Registration is required in advance for this event

See the main Symposium website for details of the symposium, including a calendar of all events occurring and how to register for a place on any course or workshop.