Let the point-line geometry Γ = (P ,L) be a half-spin geometry of type Dn,n. Then, for every embedding of Γ in the projective space P(V ), where V is a vector space of dimension 2n−1, it is true that every hyperplane of Γ arises from that embedding. It follows that any embedding of this dimension is universal. There are no embeddings of higher dimension. A corollary of this result and the fact ...

These are notes for a talk at a topology seminar at ND. 1. GENERAL FACTS In the sequel, for simplicity we denote the complex projective space CPN by PN , and we denote the projective coordinates by [~z] = [z0, . . . , zN ]. A smooth projective variety is a connected compact complex submanifold of some projective space PN . All the smooth projective varieties are Kähler manifolds, but the conver...

For an (n− 1)-Auslander algebra Λ with global dimension n, we give some necessary conditions for Λ admitting a maximal (n − 1)-orthogonal subcategory in terms of the properties of simple Λ-modules with projective dimension n − 1 or n. For an almost hereditary algebra Λ with global dimension 2, we prove that Λ admits a maximal 1orthogonal subcategory if and only if for any non-projective indecom...

In [2, Section 1.6] Peskine and Szpiro prove a theorem on adic approximations of finite free resolutions over local rings which, together with M. Artin's Approximation Theorem [1], allows them to "descend" modules of finite projective dimension over the completions of certain local rings to modules of finite projective dimension over finite etale extensions of those rings. In this note we will ...

We introduce and investigate the notion of GC -projective modules over (possibly non-noetherian) commutative rings, where C is a semidualizing module. This extends Holm and Jørgensen’s notion of C-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite GC-projectiv...

With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski’s axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least thre...