The reductions of an ideal I give a natural pathway to the properties of I, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of primary ideals. The existence of an algebra structure on the Koszul and Eagon–Northcott resolutions is the main tool for detailing the known cases of the conjecture. In the last section we relate the conjecture to a formula involving the length of the first Koszul homology modules of these ideals.

Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k

We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are quite different, being based on deformation theory.

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations de ned froma suitable ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety defined fromthe order

Abstract. This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasi-projective complex variety M. A key new result is Proposition 1.8, giving additional information on the constructible sheaf F = R 0 f∗(L), where L is a rank one

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and a recent result of Conrad we prove that the amoeba of an irreducible variety is connected. We introduce the notion of an adelic amoeba for varieties over global fields, and establish a form of the local-global principle for them. This principle is used to explain the calculation of the nonexpansive

Abstract. We give a characterization of the irreducible components of a Weierstrasstype (W -type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a

Given an n × n nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the n × n nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A, B) of n × n nilpotent matrices over K

1. Introduction. There are three types of “building blocks ” in the Bogomolov decomposition [B, Th.2] of compact Kählerian manifolds with torsion c1, namely complex tori, Calabi-Yau varieties, and irreducible symplectic manifolds. We are interested in the last type, i.e. simply-connected compact