Related papers: Coherent-Constructible Correspondence for Toric Fi…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…
We consider contact elements in the sutured Floer homology of solid tori with longitudinal sutures, as part of the (1+1)-dimensional topological quantum field theory defined by Honda--Kazez--Mati\'{c} in \cite{HKM08}. The $\Z_2$ $SFH$ of…
We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are illustrated by many interesting examples and relevant applications, while some important…
The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set $\operatorname{\mathsf{tors}} A$ of torsion classes over a finite-dimensional algebra $A$. We show that $\operatorname{\mathsf{tors}}…
There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of…
Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact…
We use the complete Segal approach to the theory of Cartesian fibrations to define and study representable Cartesian fibrations, generalizing representable right fibrations which have played a key role in $\infty$-category theory. In…
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…
We prove a microlocal counterpart of categorical localization for Fukaya categories in the setting of the coherent-constructible correspondence.
For a toric Calabi-Yau 3-orbifold relative to s Aganagic-Vafa outer branes, we prove a correspondence among the genus-zero open Gromov-Witten invariants with maximal winding at each brane and: (i) closed invariants of a toric Calabi-Yau…
We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely *within the $\infty$-category of $\infty$-categories*. We prove this is suitably compatible with the…
The main aim of the paper is to provide analogues of Simpson's correspondence on singular projective varieties defined over an algebraically closed field of characteristic $p>0$. There are two main cases. In the first case, we consider…
We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of…
We introduce the dual affine Robinson-Schensted correspondence that gives a bijection between the extended affine symmetric group and tuples $(\bar{P},\bar{Q},\lambda,N)$, where $\bar{P}$ and $\bar{Q}$ are tabloids, $\lambda$ is a…
We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and…
We study fibrations $\cV$ of toric varieties over the flag variety $G/T$, where $G$ is a compact semisimple Lie group and $T$ is a maximal torus. From symplectic data, we construct test configurations of $\cV$ and compute their Futaki…
In their paper Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours to compute certain non-trivial…
The universal Vassiliev-Kontsevich invariant is a functor from the category of tangles to a certain graded category of chord diagrams, compatible with the Vassiliev filtration and whose associated graded is an isomorphism. The Vassiliev…
Starting from the data of a nonsingular complex projective toric variety, we define an associated notion of toric co-Higgs bundle. We provide a Lie-theoretic classification of these objects by studying the interaction between Klyachko's fan…
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $\phi: X \to S$ and $\psi: Y \to S$, coincide exactly. This condition of strict equality, however, is…