WebMar 14, 2024 · Abstract. We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework … WebLet G be a Lie group and EG →BG a universal principal G-bundle. Then for any manifold M there is a 1:1 correspondence (7.2) [M,BG] ∼= −−→{isomorphism classes of principal G-bundles over M}. To a map f: M →BG we associate the bundle f∗EG →M. We gave some ingredients in the proof. For example, Theorem 6.44 proves that (7.2) is ...

Tautological classes of matroids Christopher Eur

WebThe tautological vector bundles on P(E) are similar to those on the projectivization of a vector space. The analog of the trivial bundle is the induced bundle ˇ(˘) where ˇ : P(E) !B is the projection map de-rived from p. In this bundle, the ber … Webbundles S L and Q L on the permutohedral variety X E as follows. De nition 1. The tautological subbundle S L (resp. the tautological quo-tient bundle Q L) is the unique torus … shnv pack

[2103.08021v2] Tautological classes of matroids - arxiv.org

Webgent bundles of RP(1) = S1 and RP(O) = point are trivial. Adding the trivial ri with ni =1 to other rT or i represents them as sums of line bundles. For n = 5, RP(2, 1, 0) has tangent bundle T1 @ 1 ,D which is a line bundle and two 2-plane bundles, while in all other cases there are at least two rs and the tangent bundle is a sum of line bundles. WebOct 6, 2016 · ${\rm Loc}_G(X)$ is an Artin stack over $\mathbb {C}$ ⁠, which can be viewed as a simplicial scheme over $\mathbb {C}$ ⁠.For a detailed explanation of how to interpret Artin stacks as simplicial schemes – ie., how to define sheaves, and in particular Betti cohomology, on the former via the latter – see []; for a more general treatment in the … WebMar 14, 2024 · We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for … rabbit hole darwin