Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...

We investigate the lattice $𝐋\left(𝐕\right)$ of subspaces of an $m$-dimensional vector space $𝐕$ over a finite field $\mathrm{GF}\left(q\right)$ with a prime power $q=p^n$ together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice $𝐋\left(𝐕\right)$ satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when $𝐋\left(𝐕\right)$ is orthomodular. For...