T-structures on some local Calabi–Yau varieties
By T. Bridgeland. 2005
140 citations recorded by the source corpus.
Abstract Let Z be a smooth Fano variety satisfying the condition that the rank of the Grothendieck group of Z is one more than the dimension of Z . Let ω Z denote the total space of the canonical line bundle of Z , considered as a non-compact Calabi–Yau variety. We use the theory of exceptional collections to describe t-structures on the derived category of coherent sheaves on ω Z . The combinatorics of these t-structures is determined by a natural action of an affine braid group, closely related to the well-known action of the Artin braid group on the set of exceptional collections on Z .
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3d6bd7935ddca102aa9a3a05c53ea2fede27a73b
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Citations in the corpus
- Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras (2006, background): “It also appeared in recent work of Bridgeland [ Bri2 ,3] on t-structures on the derived category of the total space of the canonical line”
- Derived categories of toric varieties III (2006, background): “useful for further investigation of the derived categories ([18], [7], [14] and [ 6 ] for example).”
- Derived equivalences from mutations of quivers with potential (2009, methodology): “ent. Using the theorem and corollary 5.5 we obtain the following corollary. Corollary 6.3. Under the hypothesis of the theorem, the category ModJ(µi(Q,W)) is obtained by tilting, in the sense of [23] [10], from the category ModJ(Q,W) at the simple module Si. Let us prove the theorem. Proof. We would”
- The space of stability conditions on the local projective plane (2009, background): “tor bundles. 28 AREND BAYER AND EMANUELE MACR`I The subcategory of D0 generated by extensions by i∗E0[2], i∗E1[1], and i∗E2 AE := hi∗E2,i∗E1[1],i∗E0[2]i is the heart of a bounded t-structure onD0. By [Bri05], the category AE can also be described as the category of nilpotent modules over a certain a”
- Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras (2012, methodology): “These mutations provide an effective method to compute the space of Bridgeland’s stability conditions on C by gluing different charts, see [14, 48].”
- Derived Categories of Toric Varieties (2005, background): “Such sheaves are useful for further investigation of the derived categories (see e.g. [6; 7; 14; 18]).”
- Constant families of t-structures on derived categories of coherent sheaves (2006, unknown): “have to be equivalent to the abelian category obtained by the tilting in the derived category of C, cf. Example 3.7 of [ 9 ].”
- The monotone wrapped Fukaya category and the open-closed string map (2012, background): “Local Calabi-Yau’s (total spaces of canonical bundles over Fano varieties) are well-known testing grounds for many aspects of mirror symmetry, with rich symplectic topology [43, 15].”
- Inducing stability conditions (2007, background): “The abelian categories Φ(〈i∗Q E 0 〉), for a Fourier-Mukai autoequivalence Φ of D b 0(X), are called in [7] quivery subcategories.”
- Dirichlet Branes and Mirror Symmetry (2009, background): “It was shown in [62] that distinct elements g ∈ G define distinct subcategories A(g) ⊂ D.”
- Helices on del Pezzo surfaces and tilting Calabi-Yau algebras (2009, background): “The tilting operation for rolled-up helix algebras was studied in [8] under the additional assumption”
- Discreteness of silting objects and t ‐structures in triangulated categories (2017, background): “It is called a simple tilt if S is simple (see [18]).”