Let R(A, R) be the degree-one resonance variety over a field R of a hyperplane arrangement A. We give a geometric description of R(A, R) in terms of projective line complexes. The projective image of R(A, R) is a union of ruled varieties, parametrized by neighborly partitions of subarrangements of A. The underlying line complexes are intersections of special Schubert varieties, easily described...

We prove various extensions of the Local Flatness Criterion over a Noetherian local ring R with residue field k. For instance, if Ω is a complete R-module of finite projective dimension, then Ω is flat if and only if Torn (Ω, k) = 0 for all n = 1, . . . , depth(R). In low dimensions, we have the following criteria. If R is onedimensional and reduced, then Ω is flat if and only if Tor1 (Ω, k) = ...

In this paper embeddings of projective Klingenberg planes in a 5-dimensional projective space are classified. It is proved that if a PK-plane is fully embedded in PG(5,K), for some skewfield K, then it is either isomorphic to the Desarguesian projective Klingenberg plane (projective Hjelmslev plane for bijective σ) PH(2,D(K, σ)) over a ring of ordinary or twisted dual numbers or it is a subgeom...

The strong no loop conjecture states that a simple module of finite projective dimension over an artin algebra has no non-zero self-extension. The main result of this paper establishes this well known conjecture for finite dimensional algebras over an algebraically closed field.

Let R = K[y] = K[y1, . . . , yn] be a polynomial ring over an arbitrary field K and let F be a finite set {f1/g1, . . . , fs/gs} of rational functions in K(y), the quotient field of R, where fi (resp. gi) is in R (resp. R \ {0}) for all i. As usual we denote the affine and projective spaces over the field K by As and Ps−1, respectively. Points of the projective space Ps−1 are denoted by [α], wh...

Let Y be a smooth projective irreducible curve defined over a finite field F q. We assume that G is a finite subgroup of the automorphism group of Y whose order divides q − 1. We show that relations among idempotents corresponding to the irreducible characters of subgroups H of G imply similar relations among generalized pranks of Y. We also relate this result to the realization of finite group...

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras of weight type other than (1, p) whose number of weights does not exceed 3. This note concerns the characterization of the canonical algebras over an algebraically closed field that are derived equivalent...

Let G be a finite group acting freely on a smooth projective scheme X over a locally compact field of characteristic 0. We show that the ε0-constants associated to symplectic representations V of G and the action of G on X may be determined from Pfaffian invariants associated to duality pairings on Hodge cohomology. We also use such Pfaffian invariants, along with equivariant Arakelov Euler cha...