Related papers: Vector bundles on Olsson fans

In this paper we answer a question posed by V.V. Batyrev. The question asked if there exists a complete regular fan with more than quadratically many primitive collections. We construct a smooth projective toric variety associated to a…

In an Archimedean directed partially ordered vector space $X$ one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover $Y$ of $X$. If $X$ has an order unit, $Y$ can be represented…

In a previous paper we introduced the notion of a {\it real semigroup} (RS) as an axiomatic framework to study diagonal quadratic forms with arbitrary entries over (commutative, unitary) semi-real rings. Two important classes of RSs were…

Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed…

This monograph is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2,n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop…

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…

Given an orthogonal bundle $E$ over a smooth projective curve $X$ we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule $L \subset…

In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…

We prove that if $V$ is a conical simple self-dual quasi-lisse vertex algebra and $M$ is an ordinary module then $\dim X_M=\dim X_V$. Hence, if moreover $X_V$ is irreducible then $X_M=X_V$. In particular, this applies to quasi-lisse simple…

This paper classifies rank two vector bundles on a del Pezzo threefold $X$ of degree five whose projectivizations are weak Fano. This classification is then used to determine properties of the moduli spaces of such vector bundles on $X$,…

This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…

Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed…

This paper studies two related subjects. One is some combinatorics arising from linear projections of polytopes and fans of cones. The other is quotient varieties of toric varieties. The relation is that projections of polytopes are related…

In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…

An Ulrich sheaf on an n-dimensional projective variety X, embedded in a projective space, is a normalized ACM sheaf which has the maximum possible number of global sections. Using a construction based on the representation theory of…

We prove that if a quasi-tilted algebra is tame, then the associated moduli spaces are products of projective spaces. Together with an earlier result of Chindris this gives a geometric characterization of the tame quasi-tilted algebras.

We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a…

We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exceptional collection of Bondal-Thomsen line bundles is invariant…

We define Reichstein transforms to be certain birational transformations of Artin stacks with good moduli spaces. Our main technical result is that the Reichstein transform of an Artin toric stack is again an Artin toric stack. This leads…

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…