Surveys in Differential Geometry

Volume 22 (2017)

Intersections of three quadrics in $\mathbb{P}^7$

Pages: 259 – 274



Brendan Hassett (Department of Mathematics, Brown University, Providence, Rhode Island, U.S.A.)

Alena Pirutka (Courant Institute, New York University, New York, N.Y., U.S.A.)

Yuri Tschinkel (Courant Institute, New York University, New York, N.Y., U.S.A.; and The Simons Foundation, New York, N.Y., U.S.A.)


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.

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The first author was partially supported by NSF grant 1551514, the second author by NSF grant 1601680, and the third by NSF grant 1601912.

Published 13 September 2018