For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.
This paper is part of the author's thesis, recently presented, where the following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series) , using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well known results for the quasi-ordinary case can be extended to this much wider family.
Let be a commutative Noetherian ring, an ideal of , an -module and a non-negative integer. In this paper we show that the class of minimax modules includes the class of modules. The main result is that if the -module is finite (finitely generated), is -cofinite for all and is minimax then is -cofinite. As a consequence we show that if and are finite -modules and is minimax for all then the set of associated prime ideals of the generalized local cohomology module...
We study the singularities of the irreducible components of the Springer fiber over a nilpotent element with in a Lie algebra of type or (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.
Recently, T. Fukui and L. Paunescu introduced a weighted version of the -regularity condition and Kuo’s ratio test condition. In this approach, we consider the - regularity condition and -regularity related to a Newton filtration.