Displaying similar documents to “Cohomology of the variational complex in the class of exterior forms of finite jet order.”

Second variational derivative of local variational problems and conservation laws

Marcella Palese, Ekkehart Winterroth, E. Garrone (2011)

Archivum Mathematicum

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We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we...

Cohomology of coherent sheaves and series of supernatural bundles

David Eisenbud, Frank-Olaf Schreyer (2010)

Journal of the European Mathematical Society

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We show that the cohomology table of any coherent sheaf on projective space is a convergent—but possibly infinite—sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.

Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents

Marcella Palese (2016)

Communications in Mathematics

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We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations...

A new infinite order formulation of variational sequences

Raffaele Vitolo (1998)

Archivum Mathematicum

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The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the...