Working with weighted complete intersections. (English) Zbl 0960.14027

Iano-Fletcher, A. R.

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

Keywords:

weighted projective space; weighted complete intersection; weighted K3 surface; weighted Fano 3-fold

Citations:

Zbl 0451.14014