相关论文: Fibre de Milnor motivique a l'infini

In this article we give an expression of the motivic Milnor fiber at infinity and the motivic nearby cycles at infinity of a polynomial $f$ in two variables with coefficients in an algebraic closed field of characteristic zero. This…

By introducing motivic Milnor fibers at infinity of polynomial maps, we propose some methods for the study of nilpotent parts of monodromies at infinity. The numbers of Jordan blocks in the monodromy at infinity will be described by the…

We compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the…

Let $P$ and $Q$ be two polynomials in two variables with coefficients in an algebraic closed field of characteristic zero. We consider the rational function $f=P/Q$. For an indeterminacy point $\text{x}$ of $f$ and a value $c$, we compute…

We study function germs on toric varieties which are nondegenerate for their Newton diagram. We express their motivic Milnor fibre in terms of their Newton diagram. We extend a formula for the motivic nearby fibre to the case of a toroidal…

We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) an element in the Grothendieck ring…

By calculating the equivariant mixed Hodge numbers of motivic Milnor fibers introduced by Denef-Loeser, we obtain explicit formulas for the Jordan normal forms of Milnor monodromies. The numbers of the Jordan blocks will be described by the…

For a polynomial $f$ in two complex variables, we prove that the multi-link at infinity of the 0-fiber $f^{-1}(0)$ is a fibred multi-link if and only if all the values different from 0 are regular at infinity.

We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These integrals are rational functions of the parameters and the…

In this paper we use motivic integration and non-archimedean analytic geometry to study the singularities at infinity of the fibers of a polynomial map $f\colon \mathbb A^d_\mathbb C \to \mathbb A^1_\mathbb C$. We show that the motive…

We find a recursive formula for the motivic Milnor fiber of an irreducible plane curve, using the notions of a truncation and derived curve. We then apply natural transformations to obtain a similar recursion for the Hodge-theoretic…

It is well known that the diffeomorphism-type of the Milnor fibration of a (Newton) non-degenerate polynomial function $f$ is uniquely determined by the Newton boundary of $f$. In the present paper, we generalize this result to certain…

We study the Jordan normal forms of the local and global monodromies over complete intersection subvarieties of $C^n$ by using the theory of motivic Milnor fibers. The results will be explicitly described by the mixed volumes of the faces…

We give a concrete formula for the total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial in most of the interesting cases. As an application, we give a description of the monodromy fibration at infinity for such kind of…

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial $f: \bR^{2n} \to \bR^2$. By using strong non-degeneracy condition, we prove a counterpart of N\'emethi and Zaharia's fibration theorem. In…

We define motivic Milnor fiber of cyclic $L_\infty$-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor…

We construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the "tropical motivic…

In this article we prove two results concerning the motivic Milnor fibres $S^{\epsilon}(f)$ associated to a map germ $f: (\mathbb{R}^n,0)\to(\mathbb{R},0)$, defined by G. Comte and G. Fichou. Firstly, we prove that if…

Let $f$ be a germ of complex analytic function at $({\mathbf{C}}^{d+1}, 0)$ such that its zero level defines an irreducible germ of quasi-ordinary hypersurface $(S,0)$. We describe the motivic Igusa zeta function, the motivic Milnor fibre…

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to…