Shramov, K. A. \( \mathbb Q\)-factorial quartic threefolds. (English. Russian original) Zbl 1132.14039 Sb. Math. 198, No. 8, 1165-1174 (2007); translation from Mat. Sb. 198, No. 7, 103-114 (2007). A variety is \(\mathbb{Q}\)-factorial when every Weil divisor has a multiple which is Cartier. Despite its technical definition, \(\mathbb{Q}\)-factoriality is crucial in many areas of MMP and higher dimensional algebraic geometry [see M. Mella, Math. Ann. 330, No. 1, 107–126 (2004; Zbl 1058.14022)]. For nodal hypersurfaces \(\mathbb{Q}\)-factoriality is equivalent to factoriality and recent results [I. Cheltsov, J. Algebr. Geom. 14, No. 4, 663–690 (2005; Zbl 1084.14039); I. Cheltsov and J. Park, Geom. Dedicata 121, 205–219 (2006; Zbl 1110.14031)] allow to conjecture a reasonable behaviour. The paper under review studies \(\mathbb{Q}\)-factoriality of nodal quartics 3-folds and prove the \(\mathbb{Q}\)-factoriality of these with at most 12 points and not containing neither a plane nor a quadric. The techniques are nice synthetic geometry constructions, and the paper is enriched by examples. Reviewer: Massimiliano Mella (Ferrara) Cited in 7 Documents MSC: 14J30 \(3\)-folds 14E05 Rational and birational maps 14E07 Birational automorphisms, Cremona group and generalizations Citations:Zbl 1058.14022; Zbl 1084.14039; Zbl 1110.14031 PDFBibTeX XMLCite \textit{K. A. Shramov}, Sb. Math. 198, No. 8, 1165--1174 (2007; Zbl 1132.14039); translation from Mat. Sb. 198, No. 7, 103--114 (2007) Full Text: DOI arXiv