On derived equivalence classes of algebraic varieties

Details On derived equivalence classes of algebraic varieties On derived equivalence classes of algebraic varieties

2006-11-17

arxiv.org/abs/math/0611545v3

Mathematics

Algebraic Geometry

19 pages, French, some typos corrected. Final version, to appear in JAG

Scientific paper

Let $X \to S$ be a miniversal family of smooth and projective varieties and D
be a fixed triangulated category. We show that the set of points s in S such
that the derived category of the fiber X_s at s is equivalent to D is at most
countable. We deduce from this that the derived equivalence classes of smooth
and projective complex varieties is at most countable.

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