An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer; Wolfgang Ebeling; Xavier Gómez-Mont

Displaying similar documents to “An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity”

On Halphen’s Theorem and some generalizations

Alcides Lins Neto (2006)

Annales de l’institut Fourier

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Let $M^{n}$ be a germ at $0 \in ℂ^{m}$ of an irreducible analytic set of dimension $n$ , where $n \geq 2$ and $0$ is a singular point of $M$ . We study the question: when does there exist a germ of holomorphic map $φ : (ℂ^{n}, 0) \to (M, 0)$ such that $φ^{- 1} (0) = {0}$ ? We prove essentialy three results. In Theorem 1 we consider the case where $M$ is a quasi-homogeneous complete intersection of $k$ polynomials $F = (F_{1}, ..., F_{k})$ , that is there exists a linear holomorphic vector field $X$ on $ℂ^{m}$ , with eigenvalues $λ_{1}, ..., λ_{m} \in ℚ_{+}$ such that $X (F^{T}) = U \cdot F^{T}$ , where $U$ is a $k \times k$ matrix with entries in $𝒪_{m}$ . We prove that if...

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...

Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite $p$ -group $G$ acting on a smooth projective curve $X$ over an algebraically closed field $k$ of characteristic $p$ , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of $G$ acting on the space $V$ of global holomorphic quadratic differentials on $X$ . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when $G$ is cyclic or when the action of $G$ on...

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

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We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ of the group algebra of the Weyl group $W_{n}$ of type $B_{n}$ containing its usual Solomon algebra and the one of $𝔖_{n}$ : $Σ^{'} (W_{n})$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to $W_{n}$ . In an appendix, P. Baumann and C. Hohlweg present in an...

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...