Course description
The geometry of projective surfaces:
Adjunction, liaison, and
classification of surfaces in P4 of small degree.
The course will use classification of surfaces in P4 of low degree as a motivating storyline to discuss important techniques in the study of projective surfaces. The main topics will be: adjunction theory, liaison, multisecant lines, special linear systems in the plane, vector bundle techniques and Heisenberg-invariant varieties.
Prerequisites:
Hartshorne, Chapter V.
Suggested reading:
Popescu, Ranestad:
Surfaces of degree 10 in the projective fourspace
via linear systems and linkage.
Aure, Decker, Hulek, Popescu, Ranestad:
Syzygies of Abelian and Bielliptic Surfaces in P4.
Abo, Ranestad:
Construction of rational surfaces of degree 12 in
projective fourspace. Journal of Algebraic Geometry 15 (2), 323-338
Lectures
2 hours three days a week, for two weeks.
(Specific times will be announced later.)
Kristian Ranestad
Kristian Ranestad is professor at the Department of Mathematics, University of Oslo. His main field of interest is projective algebraic geometry (surfaces in 4-space, varieties of small codimension, homogeneous varieties, hyperkaehler varieties, abelian varieties) and applications of algebraic geometry (elliptic curve cryptography, phylogeny and algebraic statistical models, semidefinite programming)