Related papers: Tropical vector bundles and matroids
A Steiner bundle is a vector bundle on projective space arising as the cokernel of the map defined by a matrix of linear forms. These come up in various geometric settings, and by now they are the subject of a considerable literature.…
In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being very far away from being locally trivial bundles, are at least…
We develop equivariant KK-theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce…
This paper studies a variant of Horrocks-type criteria for vector bundles mainly through a syzygy theoretic approach. Starting with explaining various proofs of the splitting criteria for ACM and Buchsbaum bundles, we are going to give new…
The Barth-Van de Ven-Tyurin-Sato Theorem claims that any finite rank vector bundle on the infinite complex projective space $\mathbf{P}^\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally…
We propose a matrix regularization of vector bundles over a general closed K\"ahler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector…
This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.
We explain how to define an embedding of a tame stack over a noetherian ring into a certain generalization of a weighted projective stack using a notion of ample vector bundle on the stack. As applications we construct algebraic moduli…
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…
This is a survey paper on the connection of enriched category theory over a quantale and tropical mathematics. Quantales or complete idempotent semirings, as well as matrices with coefficients in them, are fundamental objects in both…
We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Berget, C. Eur, H. Spink and D. Tseng to the product space…
Let X be a smooth, complete, toric variety. We study those curves C in X that are contractible, in the sense that there exists an equivariant morphism with connected fibers, with source X, that contracts exactly the irreducible curves that…
We show that in the constant coefficient case the generic tropical variety of a graded ideal exists. This can be seen as the analogon to the existence of the generic initial ideal in Groebner basis theory. We determine the generic tropical…
A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…
Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data.
Beauville asked if a compact K\"ahler manifold with split tangent bundle has a universal covering that is a product of manifolds. We use Mori theory and elementary results about holomorphic foliations to study this problem for projective…
We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…
We provide several results on the existence of metrics of non-negative sectional curvature on vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions of the…
Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes…
In this paper we prove that the cohomology of smooth projective tropical varieties verify the tropical analogs of three fundamental theorems which govern the cohomology of complex projective varieties: Hard Lefschetz theorem, Hodge-Riemann…