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Displaying similar documents to “A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation”

The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions

Ursula Ludwig (2010)

Annales de l’institut Fourier

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In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve X and a stratified Morse function f . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f .

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of d –actions (and the corresponding d -dimensional Lie algebras) defined by commuting singular vector fields in ℂ n fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of d vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

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We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...