The diagonal in a product of projective spaces is cut out by the ideal of 2×2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally reducible, and its main component is a compactification of PGL(d)/PGL(d). For n = 2 we recover the manifold of complete collineations. For projective lines ...

Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ ab(a− 1)(b− 1)/2 with the exception of the case a = b = 2, where the regularity is 4. Note that ab(a− 1)(b...

Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m . We consider multiplicities and mixed of by filtrations -primary ideals. show the theorem Teissier, Rees Sharp, Katz, characterizing equality in Minkowski inequality for ideals, true divisorial filtrations, larger category bounded filtrations. This not arbitrary

Let a be an ideal of holomorphic functions vanishing only at the origin in C. The type of a is an invariant that measures the order of vanishing of the functions in a along holomorphic curves; this invariant is of importance in the study of subelliptic estimates and subelliptic multiplier ideal sheaves. Recently there has been some interest in the question of which curves actually compute the t...

Let n and d be natural integers satisfying n ≥ 3 and d ≥ 10. Let X be an irreducible real hypersurface X in Pn of degree d having many pseudo-hyperplanes. Suppose that X is not a projective cone. We show that the arrangement H of all d − 2 pseudo-hyperplanes of X is trivial, i.e., there is a real projective linear subspace L of Pn(R) of dimension n−2 such that L ⊆ H for all H ∈ H. As a conseque...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

In this paper we study irreducible representations of regular limit subalgebras of AF-algebras. The main result is twofold: every closed prime ideal of a limit of direct sums of nest algebras (NSAF) is primitive, and every prime regular limit algebra is primitive. A key step is that the quotient of a NSAF algebra by any closed ideal has an AF C*-envelope, and this algebra is exhibited as a quot...

Let [Formula: see text] be a weighted oriented graph and its edge ideal. We provide one method to find all the minimal generators of text], where is maximal strong vertex cover intersections irreducible ideals associated covers contained in text]. If an induced digraph under certain condition on we show that for some implies necessary sufficient equality ordinary symbolic powers ideal union two...

We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. study the corresponding isotopy problem, with focus rational irreducible (rational cuspidal curves) projective plane. prove that every such is isotopic to degrees up five, and for one singularity link torus knot. Classification results classe...