D-equivalence and K-equivalence

Details D-equivalence and K-equivalence D-equivalence and K-equivalence

2002-05-27

arxiv.org/abs/math/0205287v3

Mathematics

Algebraic Geometry

25 pages, minor change

Scientific paper

Let $X$ and $Y$ be smooth projective varieties over $\mathbb{C}$. They are called {\it $D$-equivalent} if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories, while {\it $K$-equivalent} if they are birationally equivalent and the pull-backs of their canonical divisors to a common resolution coincide. We expect that the two equivalences coincide at least for birationally equivalent varieties. We shall provide a partial answer to the above problem in this paper.

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