PARUSIŃSKI , Adam

Let U be an open relatively compact subanalytic subset of a real analytic manifold M . We show that there exists a "finite linear covering" (in the sense of Guillermou- Schapira) of U by subanalytic open subsets of U homeomorphic to an open ball.We also show that the characteristic function of U can be written as a finite linear combination of...

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We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with Z/2 coefficients an analog of the weight filtration for complex algebraic varieties. This complements our previous definition of the...

International audience

International audience

We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with Z/2 coefficients an analog of the weight filtration for complex algebraic varieties. This complements our previous definition of the...

We prove lifting theorems for complex representations $V$ of finite groups $G$. Let $\sigma=(\sigma_1,\ldots,\sigma_n)$ be a minimal system of homogeneous basic invariants and let $d$ be their maximal degree. We prove that any continuous map $\bar f : \mathbb R^m \to V$ such that $f = \sigma \circ \bar f$ is of class $C^{d-1,1}$ is locally of...

We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \in \K[[X]][Z] $, $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero $\K$, and satisfying $a_1=0$, is $\nu$-quasi-ordinary. That means that if the discriminant $\Delta_P \in \K[[X]]$ is equal to a monomial times a unit then...

International audience

International audience

In this paper we show Whitney's fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratifica-tion satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization...

We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \in \K[[X]][Z] $, $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero $\K$, and satisfying $a_1=0$, is $\nu$-quasi-ordinary. That means that if the discriminant $\Delta_P \in \K[[X]]$ is equal to a monomial times a unit then...

International audience

Let $(f,g)\colon (\mathbb{C}^2,0)\longrightarrow (\mathbb{C}^2,0)$ be a holomorphic mapping with an isolated zero. We show that the initial Newton polynomial of its discriminant is determined, up to rescalling variables, by the ideals $(f)$ and $(g)$.

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We compare the topological Milnor fibration and the motivic Milnor fibre of a regular complex function with only normal crossing singularities by introducing their common extension: the complete Milnor fibration. We give two equivalent constructions: the first one extending the classical Kato-Nakayama log-space and the second one, more...

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In this paper we investigate the connections between the Lipschitz geometry of real algebraic varieties and the properties of their arc spaces.For this purpose, we first develop motivic integration in the real algebraic set-up. We construct a motivic measure on the space of real analytic arcs. We use this measure to define a real motivic...

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In this paper we prove the strong Sard conjecture for sub-Riemannian structures on 3-dimensional analytic manifolds. More precisely, given a totally nonholonomic analytic distribution of rank 2 on a 3-dimensional analytic manifold, we investigate the size of the set of points that can be reached by singular horizontal paths starting from a...