Related papers: Tate resolutions on toric varieties
Beilinson's resolution of the diagonal for complex projective space was generalized by Bayer-Popescu-Sturmfels for any unimodular toric variety. Here, we give a resolution of the diagonal for any smooth toric variety (viewed as a toric…
Using Frobenius morphisms of noncommutative blowups, we prove that every normal toric singularity has a standard noncommutative resolution.
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded…
We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also…
We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided monoidal categories. Our approach utilizes the same fan…
In this work we construct global resolutions for general coherent equivariant sheaves over toric varieties. For this, we use the framework of sheaves over posets. We develop a notion of gluing of posets and of sheaves over posets, which we…
Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties,…
We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans…
Beilinson gave a resolution of the diagonal for complex projective spaces, which Bayer-Popescu-Sturmfels generalized to what they refer to as unimodular projective toric varieties. The unimodular condition in Bayer-Popescu-Sturmfels'…
We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko…
We give a short, new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virtual resolutions and to a resolution of the diagonal in the…
We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.
Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint arXiv:math.AG/0306221. That is, they focus on the fact that toric…
We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…
We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.
In this thesis we study toric degenerations of projective varieties. We compare different constructions to understand how and why they are related as s first step towards developing a global framework. In focus are toric degenerations…
We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spaces of spatial polygons degenerate to polarized toric…
We give an explicit description of the terms and differentials of the Tate resolution of sheaves arising from Segre embeddings of $\P^a\times\P^b$. We prove that the maps in this Tate resolution are either coming from Sylvester-type maps,…
An exoflop takes a gauged Landau-Ginzburg (LG) model, partially compactifies it, and then performs certain birational transformations on it. When certain criteria hold, this can provide a crepant categorical resolution or equivalence of…
We provide a relation between the geometric framework for $q$-Painlev\'{e} equations and cluster Poisson varieties by using toric models of rational surfaces associated with $q$-Painlev\'{e} equations. We introduce the notion of seeds of…