## Working with weighted complete intersections.(English)Zbl 0960.14027

Corti, Alessio (ed.) et al., Explicit birational geometry of 3-folds. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 281, 101-173 (2000).
This article is a well-written tutorial introduction to weighted projective spaces and their subvarieties. It contains many very useful results and methods of calculation. A special place takes a derivation of the list of all anticanonically embedded weighted $${\mathbb Q}$$-Fano hypersurfaces of dimension $$3$$ (see §16.6). This list contains $$95$$ families of 3-folds which correspond 1:1 to the $$95$$ families of codimension $$1$$ weighted $$K3$$ surfaces described earlier by M. Reid in: Journées de géométrie algébrique, Angers 1979, 273-310 (1980; Zbl 0451.14014)] (see also §13.3).
For the entire collection see [Zbl 0942.00009].
Reviewer: A.Iliev (Sofia)

### MSC:

 14M10 Complete intersections

Zbl 0451.14014