SCHOOL (AND WORKSHOP) ON

ALGEBRAIC SPACE CURVES

TORINO, SEPTEMBER 23 - 27, 2002




First announcement


Lecturers.

R. Hartshorne (University of California, Berkeley, USA)
M. Martin-Deschamps (Université de Versailles, Fr)

Organizers.
The School/Workshop is organized by G. Casnati, N. Chiarli, S. Greco, R. Notari, M.L. Spreafico. For contacting the organizers send a mail to

geometri [nospam] calvino.polito.it

General informations on the School.
The school will take place at

Dipartimento di Matematica
Politecnico di Torino
c.so Duca degli Abruzzi 24
10129 Torino - Italy

It is mainly aimed to Phd students and young researchers in Algebraic Geometry.

Aim of the School.
This course will aim to cover the basic known results, and also touch on open problems, in the area of classification of algebraic curves in a projective n-space. We will discuss the possible degree and genus of curves, the Hilbert scheme, and the irreducibility of certain components. The theory of liaison is a major tool. Here we discuss the relation of the Rao module to liaison equivalence classes, minimal curves and the structure of a biliaison class, and the irreducibility of the family of curves with given postulation and Rao module. The best results are obtained in projective 3-space, while analogous results in higher dimensions are mostly conjectural.
Some open problems are the connectedness of the Hilbert scheme of locally Cohen-Macaulay curves of given degree and genus in the projective 3-space, and the problem of whether the Rao module characterizes the Gorenstein liaison class in the projective n-space for n>3.

Further announcements.
A more detailed first announcement (containing informations on accomodation, registration and financial supports) will follow probably in february.