ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: Arancibia, Jacqueline, Departmento de Matemática, UFPB–J. Pessoa, Brasil Canonical Curves in P^{3} From Riemann-Roch theorem we can conclude that a canonical curve in P^{3} is a complete intersection of a quadric and a cubic surface. This permit to define a rational map from X = {(f_{2}, g_{3}) | g_{3} is a cubic defined module a quadric f_{2}} to H ⊂ Hilb^{6t−3}P^{3} the Hilbert’s component whose generic point correspond to a canonical curve. Our goal is to extend this map to a morphism, in fact this is equivalent to construct a flat family over an appropiate variety that look likes X out of an open set. We use the same technic that in [1] and at the moment we conjecture that after 5 blowup starting from X along appropiate smooth centers we obtain the variety indicated above.

[1] J. Rojas and I. Vainsencher, Conical Sextuplrts, Communications in Algebra, 24(11), 3437-3457,1996.