Examples of Fano varieties of index one that are not birationally rigid

Castravet, Ana-Maria

doi:10.1090/S0002-9939-07-08948-4

Examples of Fano varieties of index one that are not birationally rigid
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by Ana-Maria Castravet

Proc. Amer. Math. Soc. 135 (2007), 3783-3788

DOI: https://doi.org/10.1090/S0002-9939-07-08948-4

Published electronically: September 12, 2007

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Abstract:

A conjecture of Pukhlikov states that a smooth Fano variety of dimension at least 4 and index one is birationally rigid. We show that a general member of the linear system given by the ample generator of the Picard group of the moduli space of stable, rank 2 bundles with fixed determinant of odd degree on a curve of genus at least 3 is not birationally rigid.

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