Hassett, Brendan; Pirutka, Alena; Tschinkel, Yuri Intersections of three quadrics in \(\mathbb{P}^7\). (English) Zbl 1423.14102 Cao, Huai-Dong (ed.) et al., Celebrating the 50th anniversary of the Journal of Differential Geometry. Lectures given at the Geometry and Topology Conference at Harvard University, Cambridge, MA, USA, April 28 – May 2, 2017. Somerville, MA: International Press. Surv. Differ. Geom. 22, 259-274 (2018). Summary: We study rationality properties of smooth complete intersections of three quadrics in \(\mathbb{P}^7\). We exhibit a smooth family of such intersections with both rational and non-rational fibers.For the entire collection see [Zbl 1402.14006]. Cited in 9 Documents MSC: 14E08 Rationality questions in algebraic geometry 14J35 \(4\)-folds 14M10 Complete intersections PDFBibTeX XMLCite \textit{B. Hassett} et al., Surv. Differ. Geom. 22, 259--274 (2018; Zbl 1423.14102) Full Text: DOI arXiv