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


Author: Ana-Maria Castravet
Journal: Proc. Amer. Math. Soc. 135 (2007), 3783-3788
MSC (2000): Primary 14E07; Secondary 14H60
DOI: https://doi.org/10.1090/S0002-9939-07-08948-4
Published electronically: September 12, 2007
MathSciNet review: 2341927
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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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Additional Information

Ana-Maria Castravet
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003
Email: noni@math.utexas.edu, noni@math.umass.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08948-4
Received by editor(s): May 5, 2006
Received by editor(s) in revised form: September 17, 2006
Published electronically: September 12, 2007
Communicated by: Ted Chinburg
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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