A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

 The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...

In this paper, we study the problem when a finitely generated torsionless module is projective. Let Λ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless Λ-module M is projective if Ext Λ (M,M) = 0. For a commutative Artinian ring Λ, a finitely generated torsionless Λ-module M is projective if the following conditions are satisfied: (1) Ext Λ (M,Λ) = 0 f...

We study Enriques surfaces with four disjoint A2-configurations. In particular, we construct open Enriques surfaces with fundamental groups (Z/3Z) × Z/2Z and Z/6Z, completing the picture of the A2-case from [10]. We also construct an explicit Gorenstein Q-homology projective plane of singularity type A3 + 3A2, supporting an open case from [7].

We prove a vanishing theorem for the Hodge number h of projective toric varieties provided by a certain class of polytopes We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope In particular the vanishing theorem for h implies that these deformations are unobstructed

We recall the basic geometric properties of the projective variety Latn r (K) parametrizing a family of special lattices over Witt vectors proved in [Hab05, HS, San04]. In this paper, we prove that a particular set of subvarieties of Latn r (K) are normal and Gorenstein. The set contains the subregular variety, that is, the complement of the smooth locus, of Latn r (K).