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

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

2006-04-26

arxiv.org/abs/math/0604548v2

Mathematics

Algebraic Geometry

4 pages; final version, to appear in Proc. of AMS

Scientific paper

A conjecture of Pukhlikov states that a smooth Fano variety of dimension at
least four 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 two bundles with fixed determinant of odd degree
on a curve of genus at least three, is not birationally rigid.

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