Displaying similar documents to “The set of points at which a morphism of affine schemes is not finite”

Vertex algebras and the formal loop space

Mikhail Kapranov, Eric Vasserot (2004)

Publications Mathématiques de l'IHÉS

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We construct a certain algebro-geometric version ℒ ( X ) of the free loop space for a complex algebraic variety X. This is an ind-scheme containing the scheme ℒ 0 ( X ) of formal arcs in X as studied by Kontsevich and Denef-Loeser. We describe the chiral de Rham complex of Malikov, Schechtman and Vaintrob in terms of the space of formal distributions on ℒ ( X ) supported in ℒ 0 ( X ) . We also show that ℒ ( X ) possesses a factorization structure: a certain non-linear version of a vertex algebra structure. This explains...

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.