We give an explicit construction, for a flat map X → S of algebraic spaces, of an ideal in the n’th symmetric product of X over S. Blowing up this ideal is then shown to be isomorphic to the schematic closure in the Hilbert scheme of length n subschemes of the locus of n distinct points. This generalises Haiman’s corresponding result ([13]) for the affine complex plane. However, our constructio...

In this paper we prove that the Hausdorff dimension function of the limit sets of strongly regular, countable, conformal graph directed Markov systems living in higher dimensional Euclidean spaces R, d ≥ 3, and with an underlying finitely irreducible incidence matrix is real-analytic.

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

In this paper we prove that the Hausdorff dimension function of the limit sets of strongly regular, hyperbolic, conformal graph directed Markov systems living in higher dimensional Euclidean spaces R, d ≥ 3, and with an underlying finitely irreducible incidence matrix is real-analytic.

We generalize a result of Kostant and Wallach concerning the algebraic integrability of the Gelfand-Zeitlin vector fields to the full set of strongly regular elements in gl(n, C). We use decomposition classes to stratify the strongly regular set by subvarieties XD. We construct an étale cover ĝD of XD and show that XD and ĝD are smooth and irreducible. We then use Poisson geometry to lift the G...

Let $$L_n$$ be a line graph with n edges and $${{\mathcal {F}}}(L_n)$$ the facet ideal of its matching complex. In this paper, we provide irreducible decomposition some exact formulas for projective dimension regularity .

We consider generalizations of Schützenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weight...

Suppose that a three-manifold M contains infinitely many distinct strongly irreducible Heegaard splittings H + nK, obtained by Haken summing the surface H with n copies of the surface K. We show that K is incompressible. All known examples, of manifolds containing infinitely many irreducible Heegaard splittings, are of this form. We also give new examples of such manifolds.

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. We are concerned with the following question: Which algebras are homomorphic images of subdirectly irreducible algebras? A necessary condition, discovered...