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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].

MSC:

14E08 Rationality questions in algebraic geometry
14J35 \(4\)-folds
14M10 Complete intersections
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