Birational rigidity is not an open property

Abstract

We construct an example of the birationally rigid complete intersection of a quadric and a cubic in $\PA^5$ with an ordinary double point, which under a small deformation gives a non-rigid Fano variety. Thus we show that birational rigidity is not open in moduli.

26 pages

References in corpus (2)

• Divisorial contractions in dimension three which contract divisors to smooth points
• Q-factorial quartic threefolds

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