Related papers: The theory of tight closure from the viewpoint of …

In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain…

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…

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…

The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.

These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…

The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…

Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…

We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…

We construct a vector bundle $E$ on a smooth complex projective surface $X$ with the property that the restriction of $E$ to any smooth closed curve in $X$ admits an algebraic connection while $E$ does not admit any algebraic connection.

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field…

In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.

An introduction to the theory of bundle gerbes and their relationship to Hitchin-Chatterjee gerbes is presented. Topics covered are connective structures, triviality and stable isomorphism as well as examples and applications.

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.

Tangent categories offer a categorical context for differential geometry, by categorifying geometric notions like the tangent bundle functor, vector fields, Euclidean spaces, vector bundles, connections, etc. In the last decade, the theory…

We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, which provide the necessary algebraic background for the theory…

We show that one can achieve transversality for lifts of holomorphic disks to a projectivized vector bundle by locally enlarging the structure group and considering the action of gauge transformations on the almost complex structure, which…

We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…

We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle on X is…