Families of hypersurfaces with many prescribed singularities [Elektronische Ressource] / Eric Westenberger

Families of hypersurfaces with manyprescribed singularitiesEric WestenbergerVom Fachbereich Mathematik der Universit at Kaiserslauternzur Verleihung des akademischen Grades Doktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.) genehmigte Dissertation1. Gutachter: Prof. Dr. G.-M. Greuel2.hter: Prof. Dr. E. ShustinVollzug der Promotion: 18.06.2004D 386The image on the title page shows the surface of degree 8 de ned by the equation4 2 2 4 2 2 4 2 2(x x + 1) + (y y + 1) + (z z + 1) = 1:It has 144 real ordinary double points. The equation is similar to Chmutov’s construction[Ch92], and I would like to thank O. Labs for showing it to me.The image was produced using the programme Surf written by S. Endrass.Families of hypersurfaces withmany prescribed singularitiesEric WestenbergerVom Fachbereich Mathematikder Universit at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. G.-M. Greuel2.hter: Prof. Dr. E. ShustinVollzug der Promotion: 18.06.2004D 386IntroductionStudying varieties with prescribed properties is one of the fundamental tasks inalgebraic geometry. It was one of the main achievements in the last century torealize that it is not only necessary to study these varieties for themselves, but alsoto consider families of varieties.