Equivalences and Stratified Flops
نویسنده
چکیده
We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A).
منابع مشابه
Flops 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 کاملWindow Shifts, Flop Equivalences and Grassmannian Twists
We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel-Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well-suited to explicit computations. We then give a geometric ...
متن کاملN ov 2 00 2 Flops of G - Hilb and equivalences of derived categories by variation of GIT quotient
For a finite subgroup G ⊂ SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C3/G. This paper considers the moduli spaces Mθ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G -Hilb for a particular choice of GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C...
متن کاملar X iv : m at h / 02 07 17 0 v 1 [ m at h . A G ] 1 9 Ju l 2 00 2 THREE - DIMENSIONAL FLOPS AND NON - COMMUTATIVE RINGS MICHEL
For Y, Y + three-dimensional smooth varieties related by a flop, Bondal and Orlov conjectured that the derived categories D b (coh(Y)) and D b (coh(Y +)) are equivalent. This conjecture was recently proved by Bridge-land. Our aim in this paper is to give a partially new proof of Bridgeland's result using non-commutative rings. The new proof also covers some mild singular and higher dimensional ...
متن کاملUniversal Derived Equivalences of Posets of Tilting Modules
We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their tilting modules are related by a simple combinatorial construction, which we call flip-flop. We deduce that the posets of tilting modules of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent.
متن کامل