Algebraic Local Cohomology Classes Attached to Unimodal Singularities

TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...

Torsion cohomology classes and algebraic cycles on complex projective manifolds

Let X be a smooth complex projective manifold and H(X,Z) its singular cohomology group of degree n, with integral coefficients. Given a torsion class α ∈ H(X,Z), can we say that this class α is algebraic? This is true when k = 1, and, apparently, Hodge thought that this would always be the case [10]. However, Atiyah and Hirzebruch found counterexamples to Hodge’s assertion [2]. This is why the ...

A Cohomology Attached to a Function

In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and we prove that it satisfies both the excision and the Mayer-Vietoris axioms. For a regular function we show that the cohomology is related to the de Rham cohomology. Finally, we use it to give a new proof of a well-know...

On Reducing sequences and an Application to Local Cohomology Modules

Invariant Symmetries of Unimodal Function Singularities

We classify finite order symmetries g of the 14 exceptional unimodal function singularities f in 3 variables, which satisfy a so-called splitting condition. This means that the rank 2 positive subspace in the vanishing homology of f should not be contained in one eigenspace of g⋆. We also obtain a description of the hyperbolic complex reflection groups appearing as equivariant monodromy groups ...