Related papers: Canonical tilting bundles: the first nonabelian ex…
Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities. In this paper, we give a…
We show how to construct tilting bundles for a class of smooth projective varieties using characteristic $p$ methods. Given such a variety $X$, reduce it modulo a prime number and consider the direct image of the structure sheaf under the…
In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well as a tilting…
In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal…
We identify two distinct approaches to the derived equivalence for the stratified Mukai flop of cotangent bundles of Grassmannians -- one induced by the geometric categorical sl(2) action, and the other through the magic window category of…
This paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth $4$-dimensional toric Fano varieties. The tilting bundles lead to a large class of explicit Calabi-Yau-$5$ algebras,…
A theorem of the first author states that the cotangent bundle of the type $A$ Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety. We extend this result to cotangent…
Using geometrical correspondences induced by projections and two-steps flag varieties, and a generalization of Orlov's projective bundle theorem, we relate the Hodge structures and derived categories of subvarieties of different…
Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also construct all crepant resolutions of the above variety. We give an explicit toric…
We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.
Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting…
In this paper we give a survey of various results about the topology of oriented Grassmannian bundles related to the exceptional Lie group G_2. Some of these results are new. We give self-contained proofs here. One often encounters these…
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…
The aim of these notes is to describe how to construct canonical bundles of moving frames and differential invariants for parametrized curves in Lagrangian Grassmannians, at least in the monotonic case. Such curves appear as Jacobi curves…
Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…
We say that an exact equivalence between the derived categories of two algebraic varieties is tilting-type if it is constructed by using tilting bundles. The aim of this article is to understand the behavior of tilting-type equivalences for…
We construct a tilting object for the stable category of vector bundles on a weighted projective line X of type (2,2,2,2;\lambda), consisting of five rank two bundles and one rank three bundle, whose endomorphism algebra is a canonical…
We generalize, explain and simplify Langer's results concerning Frobenius direct images of line bundles on quadrics, describing explicitly the decompositions of higher Frobenius push-forwards of arithmetically Cohen-Macaulay bundles into…
We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…
Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…