A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hi...

Huw Price has argued that on an interventionist account of cause the dis1 tinction is perspectival, and the claim prompted some interesting responses from 2 interventionists and in particular an exchange with Woodward that raises questions 3 about what it means to say that one or another structure is perspectival. I’ll introduce 4 his reasons for claiming that the distinction between cause and ...

This article is an introduction to two fundamental primitives in cryptographic protocol theory: commitment schemes and zero-knowledge protocols, and a survey of some new and old results on their existence and the connection between them. 1 What’s in this article? This article contains an introduction to two fundamental primitives in cryptographic protocol theory: commitment schemes and zero-kno...

The moduli spaces of semistable torsion-free sheaves with c 1 = 0 and c 2 = ?2 and ?3 over a principally polarised complex torus are described explicitly in terms of zero-dimensional subschemes of the torus. The boundary structures are computed in detail. The rst moduli space is a compactiied family of Jacobians and the second is a Hilbert scheme. In this paper we shall show how detailed inform...

In an earlier paper [KRS] we defined and investigated the properties of the näıve blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one näıvely blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noether...