ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Gattazzo, Remo, University of Padua, Italy Almost factorial quartic surfaces in ℙ_{ℂ}^{3} with a tacnodal point Noether, Andreotti, Deligne proved that any algebraic curve on the generic algebraic quartic surface F in ℙ_{ℂ}^{3} is a complete intersection of F with another surface, i. e. ℂ[F] is factorial. Our problem is: find the normal quartic surfaces F such that any curve on it is a set-theoretic complete intersection, i. e. ℂ[F] is almostfactorial. Normal quartic surfaces in ℙ_{ℂ}^{3} with a triple or quadruple point have already been classified. Here we find seven families of almostfactorial quartic surfaces F endowed with an isolated double point of tacnodal type. For each curve C on F a way to compute a surface G such that F ∩ G = C is given. For five families it results I(C, F ∩ G) ≤ 4 and I(C, F ∩ G) ≤ 12 for the others.