Motivic and quantum invariance under stratified Mukai flops
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...
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We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A).
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In the joint paper [8] with Y.-P. Lee and C.-L. Wang, we have shown that the big quantum ring is invariant under P flops of splitting type, after an analytic continuation over the extended Kähler moduli space. It is a generalization of our previous work for the case of simple P flops [7]. In this note, I would like to outline the results and concentrate mainly on the detailed study of a simple ...
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...
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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: Journal of Differential Geometry
سال: 2008
ISSN: 0022-040X
DOI: 10.4310/jdg/1221066632