Vector bundles and finite covers
نویسندگان
چکیده
Abstract Motivated by the problem of finding algebraic constructions finite coverings in commutative algebra, Steinitz realization number theory and study Hurwitz spaces geometry, we investigate vector bundles underlying structure sheaf a flat branched covering. We prove that, up to twist, every bundle on smooth projective curve arises from direct image smooth, connected cover.
منابع مشابه
Locally trivial quantum vector bundles and associated vector bundles
We define locally trivial quantum vector bundles (QVB) and construct such QVB associated to locally trivial quantum principal fibre bundles. The construction is quite analogous to the classical construction of associated bundles. A covering of such bundles is induced from the covering of the subalgebra of coinvariant elements of the principal bundle. There exists a differential structure on the...
متن کاملToric Vector Bundles, Branched Covers of Fans, and the Resolution Property
We associate to each toric vector bundle on a toric variety X(∆) a “branched cover” of the fan ∆ together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric Cartier divisors and piecewise-linear functions. We apply this combinatorial geometric technique to study the moduli of toric vector bundles with fixed equivariant Ch...
متن کاملEssentially Finite Vector Bundles on Varieties with Trivial Tangent Bundle
Let X be a smooth projective variety, defined over an algebraically closed field of positive characteristic, such that the tangent bundle TX is trivial. Let FX : X −→ X be the absolute Frobenius morphism of X. We prove that for any n ≥ 1, the n–fold composition Fn X is a torsor over X for a finite group–scheme that depends on n. For any vector bundle E −→ X, we show that the direct image (Fn X)...
متن کاملFinite rank vector bundles on inductive limits of grassmannians
If P is the projective ind-space, i.e. P is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on P is isomorphic to a direct sum of line bundles. We extend this theorem to general sequences of morphisms between projective spaces by proving that, if there are infinitely many morphisms of de...
متن کاملAlmost-free finite covers
Let W be a first-order structure and ρ be an Aut(W )-congruence on W . In this paper we define the almost-free finite covers of W with respect to ρ, and we show how to construct them. These are a generalization of free finite covers. A consequence of a result of [5] is that any finite cover of W with binding groups all equal to a simple non-abelian permutation group is almostfree with respect t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2022
ISSN: ['2050-5094']
DOI: https://doi.org/10.1017/fms.2022.19