Surveys in Differential Geometry

Volume 22 (2017)

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

Pages: 259 – 274

DOI: https://dx.doi.org/10.4310/SDG.2017.v22.n1.a9

Authors

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.)

Abstract

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.

Published 13 September 2018