Lin, Jiayuan Birational unboundedness of \({\mathbb Q}\)-Fano threefolds. (English) Zbl 1019.14005 Int. Math. Res. Not. 2003, No. 6, 301-312 (2003). From the introduction: We work over an algebraically closed field of characteristic zero.Definition 1.1. Let \(X\) be a projective variety, \(X\) is said to be a \(\mathbb{Q}\)-Fano variety, if(1) \(X\) has \(\mathbb{Q}\)-factorial log terminal singularities, and(2) \(-K_X\) is ample.The reader is referred to [a paper by J. McKernan [“Boundedness of log terminal Fano pairs of bounded index” (preprint: http://front.math.ncdavis.edu/math.AG/0205214)] for the standard definitions of higher-dimension geometry, such as log terminal. The main goal of this paper is to prove the following main theorem.Theorem 1.2. The family of \(\mathbb{Q}\)-Fano threefolds with Picard number one is birationally unbounded. Cited in 5 Documents MSC: 14E05 Rational and birational maps 14J30 \(3\)-folds 14J32 Calabi-Yau manifolds (algebro-geometric aspects) Keywords:Fano threefolds; log terminal singularities PDFBibTeX XMLCite \textit{J. Lin}, Int. Math. Res. Not. 2003, No. 6, 301--312 (2003; Zbl 1019.14005) Full Text: DOI arXiv Link