Mukai 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 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...
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 کاملScalar Extensions of Derived Categories and Non-fourier-mukai Functors
Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. This result has been extended by Lunts and Orlov to include functors from perfect complexes to quasi-coherent complexes. In this paper we show that the latter extension is false without the ful...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2003
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2003.061