相关论文: L\^e Modules and Traces

For primes $p\ge 7$, we give a parametrization of the filtered $\varphi$-modules attached to the $p$-adic Tate modules of abelian surfaces over $\mathbb{Q}_p$ with supersingular good reduction. We use this classification to determine the…

The structure of the BP<n>-cohomology of elementary abelian p-groups is studied, obtaining a presentation expressed in terms of BP-cohomology and mod-p singular cohomology, using the Milnor derivations. The arguments are based on a result…

Given a nonconstant polynomial map over the reals having an isolated critical point in the origin and with zero locus of positive dimension, we establish a formula for the singular homology groups of a Milnor fibre relative to its boundary.

Combining recent results by A. Macinic, S. Papadima and R. Popescu with a spectral sequence and computer aided computations, we determine the monodromy action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the hyperplane…

In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free $\mathbb{Z}_2$ and…

We use covering space theory and the fundamental group of complements of complexified-real line arrangements to explore the associated Milnor fiber. This work yields a combinatorially determined upper bound on the rank of the first homology…

For a family of varieties, we prove that the alternating sum of the traces of "local" monodromy acting on the $\ell$-adic \'etale cohomology groups of the generic fiber is an integer which is independent of $\ell$.

A general vanishing result for the first cohomology group of affine smooth complex varieties with values in rank one local systems is established. This is applied to the determination of the monodromy action on the first cohomology group of…

For a germ $f$ on a complex manifold $X$, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness criterion. We use this Liouville complex to connect properties of the…

mu-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms…

For a real reflection group the reflecting hyperplanes cut out on the unit sphere a simplicial complex called the Coxeter complex. Abramenko showed that each reflecting hyperplane meets the Coxeter complex in another Coxeter complex if and…

We show that the base spaces of the semiuniversal unfoldings of some weighted homogeneous singularities can be identified with moduli spaces of $A_\infty$-structures on the trivial extension algebras of the endomorphism algebras of the…

Each complex hyperplane arrangement $\mathcal{A}$ gives rise to a Milnor fibration of its complement. Building on work of Zuber, we give a combinatorial sufficient condition for the Milnor fiber $F(\mathcal{A})$ to be non-$1$-formal,…

In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property…

We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of…

Let $\{f_t\}$ be a family of complex polynomial functions with line singularities. We show that if $\{f_t\}$ has a uniform stable radius (for the corresponding Milnor fibrations), then the L\^e numbers of the functions $f_t$ are independent…

In this note we consider the Milnor fiber $F$ associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$,…

We prove that for any germ of complex analytic set in $\CC^n$ there exists a hypersurface singularity whose Milnor fibration has trivial geometric monodromy and fibre homotopic to the complement of the germ of complex analytic set. As an…

We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve $C$. The relation to the zero set of Bernstein-Sato polynomial of the defining homogeneous…

We introduce the theory of local and global monodromies of polynomials in cohomology groups in various geometric situations, focusing on its relations with toric geometry and motivic Milnor fibers, and moreover in the modern languages of…