Date of Award
Spring 2019
Document Type
Open Access Dissertation
Department
Mathematics
First Advisor
Jesse Kass
Second Advisor
Ralph Howard
Abstract
In this thesis, we use the Clebsch map to construct cubic surfaces with twenty-seven lines in PG(3, q) from 6 points in general position in PG(2, q) for q = 17, 19, 23, 29, 31. We classify the cubic surfaces with twenty-seven lines in three dimensions (up to e- invariants) by introducing computational and geometrical procedures for the classi- fication. All elliptic and hyperbolic lines on a non-singular cubic surface in PG(3, q) for q = 17, 19, 23, 29, 31 are calculated. We define an operation on triples of lines on a non-singular cubic surface with 27 lines which help us to determine the exact value of the number of Eckardt point on a cubic surface. Moreover, we discuss the irreducibil- ity of classes of smooth cubic surfaces in PG(19, C), and we give the corresponding codimension of each class as a subvariety of PG(19, C).
Rights
© 2019, Mohammed Alabbood
Recommended Citation
Alabbood, M.(2019). Classification of Non-Singular Cubic Surfaces up to e-invariants. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/5225