Instructional Workshop
Surfaces: Geometry and Arithmetic
Monday 14 AprilFriday 18 April
at the
Mathematics Research Centre,
University of Warwick, UK
Organizers/Instructors
Martin Bright, Ronald van Luijk, Samir Siksek, Damiano Testa
Format
There will be three instructional lectures every morning. In the afternoon the
participants will have the opportunity to work on exercises in groups.
Programme pdf
Monday:
 Bright: Picard groups, definition and simple examples
(P^2, quadric surface in P^3)
notes (pdf)
 van Luijk:
Canonical divisor on hypersurface of degree d in P^n
and on complete intersections; very ample divisors notes (pdf)
 Testa: Classification and the minimal model program; the Hodge diamond notes (pdf)

Exercises 1 (pdf)
Tuesday:
 Bright: RiemannRoch on surfaces, genus and effectivity of
(1)curves, adjunction formula
 van Luijk: Picard groups of del Pezzo surfaces notes (pdf)

Testa: Root Lattices and their automorphism groups; SegreManin for del Pezzo surfaces I
notes (pdf)

Exercises 2 (pdf)
Wednesday:
 Testa: SegreManin for del Pezzo surfaces II
 van Luijk: Growth of rational points
 Bright: Explicitly computed examples of BrauerManin obstruction through
quadratic reciprocity
notes (pdf)
Thursday:
Friday:
 van Luijk
Galois Cohomology II
 Bright and Testa:
How to find the algebra from Galois cohomology?
Magma Program
Prerequisites. Some familiarity with basic algebraic
and arithmetic geometry is assumed, at the level of the
first two chapters of Silverman's book "Arithmetic of Elliptic
Curves".
Preliminary Reading.
Participants may find it
helpful to work through the first few chapters of
"Chapters on Algebraic Surfaces" by Miles Reid
(available online).
Preliminary reading on group cohomology will
also be useful, a good reference is chapter 2 of
Milne's notes on Class Field Theory.
Registration is now closed
Particpants from universities belonging to the
GTEM
network might be able to obtain travel and
accommodation expenses from GTEM; please contact your
local scientistincharge.
Samir Siksek