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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
The theorem about 27 lines
 Till, Daniel ; Šťovíček, Jan (advisor) ; Příhoda, Pavel (referee)
In this work we will prove there are exactly 27 different lines on each non- singular cubic surface over an agebraically closed field not of characteristic two. Firstly, we will focus on affine algebraic varieties and their ideals. We will prove Hilbert's Nullstellensatz and introduce morphisms between affine algebraic va- rieties. Then we move on to projective algebraic varieties and their ideals. We introduce morphisms between projective varieties and nomenclature for selected types of projective varieties. We will prove auxiliary statements about intersection of two distinct lines in a projective plane, respectively a line and a plane in P3 K. We also define concepts such as a tangent space to variety at a given point, sin- gularity of a hypersurface and irreducible variety. Then we move to P3 K, where we will prove the existence of 27 different lines on any nonsingular cubic surface. We will firstly prove that there is a line on such a surface and then we construct all 27 lines by mutual relations. 1
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