Displaying similar documents to “Trivial noncommutative principal torus bundles”

Product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2001)

Colloquium Mathematicae

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A complete description is given of all product preserving gauge bundle functors F on vector bundles in terms of pairs (A,V) consisting of a Weil algebra A and an A-module V with d i m ℝ ( V ) < ∞ . Some applications of this result are presented.

A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let X be a smooth projective curve defined over an algebraically closed field k , and let F X denote the absolute Frobenius morphism of X when the characteristic of k is positive. A vector bundle over X is called virtually globally generated if its pull back, by some finite morphism to X from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of k is positive, a vector bundle E over X is virtually globally generated if and only...

On the fiber product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2003)

Annales Polonici Mathematici

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We present a complete description of all fiber product preserving gauge bundle functors F on the category m of vector bundles with m-dimensional bases and vector bundle maps with local diffeomorphisms as base maps. Some corollaries of this result are presented.

About G -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

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Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G ( X ) parametrizing S -equivalence classes of semistable G -bundles over an elliptic curve X is isomorphic to [ Γ ( T ) ⊗ Z X ] / W . By a result of Looijenga, this shows that M G ( X ) is a weighted projective space.

On quasijet bundles

Tomáš, Jiří

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In this paper a Weil approach to quasijets is discussed. For given manifolds M and N , a quasijet with source x ∈ M and target y ∈ N is a mapping T x r M → T y r N which is a vector homomorphism for each one of the r vector bundle structures of the iterated tangent bundle T r [, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by Q J r ( M , N ) the bundle of quasijets from M to N ; the space J ˜ r ( M , N ) of non-holonomic r -jets from M to N is embeded into Q J r ( M , N ) . On the other hand, the bundle Q T m r N of ( m , r ) -quasivelocities...

Line bundles with c 1 ⁢ L 2 = 0

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove that on a C ⁢ W -complex the obstruction for a line bundle L to be the fractional power of a suitable pullback of the Hopf bundle on a 2-dimensional sphere is the vanishing of the square of the first Chern class of L . On the other hand we show that if one looks at integral powers then further secondary obstructions exist.