Projectively Normal but Superabundant Embeddings of Rational Surfaces in Projective Space

On non-projective normal surfaces

In this note we construct examples of non-projective normal proper algebraic surfaces and discuss the somewhat pathological behaviour of their Neron-Severi group. Our surfaces are birational to the product of a projective line and a curve of higher genus.

Embeddings of Surfaces in Euclidean Three-space

Smooth Kummer Surfaces in Projective Three-space

In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree. Introduction Let X be a smooth quartic surface in projective three-space P. As a consequence of Nikulin’s theorem [6] X is a Kummer surface if and only if it contains sixteen mutually disjoint smooth rational curves. The classic...

Construction of Rational Surfaces of Degree 12 in Projective Fourspace

The aim of this paper is to present two different constructions of smooth rational surfaces in projective fourspace with degree 12 and sectional genus 13. In particular, we establish the existences of five different families of smooth rational surfaces in projective fourspace with the prescribed invariants.

Embeddings of Projective Klingenberg Planes in the Projective Space PG(5,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...