(Classification of algebraic quartic surfaces possessing a one dimensional family of conics)
diploma thesis1 by Sebastian Oehms, 12.1.1990
Abstract:
The investigation of quartic surfaces possessing a one dimensional algebraic family of conics was started by E. Kummer in 1865. He described all types of such surfaces except two of them. These two missing types the singular loci of which consist just of isolated singularities have been found by C.M. Jessop (1916) and W.F. Meyer (1921-34) respectively. On the one hand in none of these works the completeness of the given classification is claimed. On the other hand, for some of the types the family of conics degenerates to a family of pairs of straight lines. Moreover, there are surfaces in their lists which don't contain any irreducible conic at all. In this work the completeness of the list given by W.F. Meyer is shown. Furthermore the surfaces possessing a family of irreducible conics are singled out. In some cases all families of conics and in some cases all conics are determined.