Flops and derived categories
نویسندگان
چکیده
منابع مشابه
2 Mukai flops and derived categories
In this note, we shall prove that two smooth projective varieties of dim 2n connected up by a Mukai flop have equivalent bounded derived categories of coherent sheaves. More precisely, let X and X be smooth projective varieties of dimension 2n such that there is a birational map φ : X −− → X obtained as the Mukai flop along a subvariety Y ⊂ X which is isomorphic to P. By definition, φ is decomp...
متن کاملun 2 00 2 Mukai flops and derived categories
Derived categories possibly give a new significant invariant for algebraic varieties. In particular, when the caninical line bundle is trivial, there are varieties which are not birationally equivalent, but have equivalent derived categories. The most typical example can be found in the original paper [Mu]. On the other hand, for such varieties, it is hoped that the birationally equivalence sho...
متن کاملFlops and Equivalences of derived Categories for Threefolds with only terminal Gorenstein Singularities
The main purpose of this paper is to show that Bridgeland’s moduli space of perverse point sheaves for certain flopping contractions gives the flops, and the Fourier-Mukai transform given by the birational correspondence of the flop is an equivalence between bounded derived categories.
متن کامل6 M ay 2 00 3 Mukai flops and derived categories II
If Problem 2 is affirmative, then, which functor gives the equivalence ? The following examples suggest that the functor Ψ defined by the fiber product X ×X̄ X + would be a correct one. Examples. (1) ([B-O]): Let X be a smooth quasi-projective variety of dimension 2h−1 which contains a subvarietyM ∼= P with NM/X ∼= O(−1) . One can blow up X along M and blow down the exceptional divisor in anothe...
متن کامل. A G ] 2 9 Ju l 2 00 3 Mukai flops and derived categories II
If Problem 2 is affirmative, then, which functor gives the equivalence ? The following examples suggest that the functor Ψ defined by the fiber product X ×X̄ X + would be a correct one. Examples. (1) ([B-O]): Let X be a smooth quasi-projective variety of dimension 2h−1 which contains a subvarietyM ∼= P with NM/X ∼= O(−1) . One can blow up X along M and blow down the exceptional divisor in anothe...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2002
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220100185