Any line is associated with a two-parameter group of polar complexes relative to a given first-order line complex that are called tangential complexes when the line belongs to the complex. The congruence that is determined by the tangential complex of a complex line is of a special kind, in that both of its directrices coincide in a single line that is the complex line itself. It is of a specia...

We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a circle with Dirichlet boundary conditions. We also show that moduli parameters of singular surfaces coincide with those of smooth surfaces with boundaries. S...