Related papers: 25 open questions about vector bundles and their m…
We consider global generation of sheaves of coinvariants on the moduli space of curves given by simple modules over certain vertex operator algebras, extending results for affine VOAs at integrable levels on stable pointed rational curves.…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
In order to unify the construction of the moduli space of vector bundles with different types of global decorations, such as Higgs bundles, framed vector bundles and conic bundles, A. Schmitt introduced the concept of a swamp. In this work,…
In this paper, we study moduli spaces of 2-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.
The moduli spaces for Higgs bundles associated to real Lie groups and a closed Riemann surface have multiple connected components. This survey provides a compendium of results concerning the counting of these components in cases where the…
We obtain effective results for the global generation of pluritheta line bundles on moduli spaces of vector bundles on curves. The main ingredient is an independent result giving an upper bound on the dimension of the Hilbert scheme of…
In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected…
In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on…
Let $k$ be an algebraically closed field of any characteristic, and let $(X,P)$ be an orbifold curve over $k$. We construct the moduli space $\mathrm{M}_{(X,P)}^{\mathrm{ss}}(n, \Delta)$ of $P$-semistable bundles on $(X,P)$ of rank $n$ and…
We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach…
Le but cette note est de tenter d'expliquer les liens \'etroits qui unissent la th\'eorie des empilements de cercles et des modules combinatoires, et de comparer les approches \`a la conjecture de J.W. Cannon qui en d\'ecoulent. ???? The…
Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
We investigate the geometry and topology of a standard moduli space of stable bundles on a Riemann surface, and use a generalization of the Verlinde formula to derive results on intersection pairings.
The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…
We have studied irreducible Hom-Lie algebroid connections for Hom-bundle and prove that the H-gauge theoretic moduli space has a Hausdorff Hilbert manifold structure. This work generalizes some known results about simple semi-connections…
This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…
We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the…
We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over…
In this paper differential operators on various moduli spaces (e.g. of holomorphic vector bundles) are described in a canonical way in terms of the geometry of a certain distinguished completion of an appropriate configuration space.