This thesis is about rational points on so-called del Pezzo surfaces, which are a certain type of surfaces with relatively simple geometry. The lower the degree of a del Pezzo surface, the more...Show moreThis thesis is about rational points on so-called del Pezzo surfaces, which are a certain type of surfaces with relatively simple geometry. The lower the degree of a del Pezzo surface, the more intricate is its geometry. Let S be a del Pezzo surface over a field k. It is known that if the degree of S is not 1 and S(k) is non-empty (with a mild extra condition for degree 2), the surface S is k-unirational, meaning that there is a dominant rational map from some projective space to S. If k is an infinite field, this implies that the set S(k) of k-rational points lies Zariski dense in S. But in general, we do not know whether unirationality holds when the degree is 1, and the answer to this question seems way out of reach. So if we want to prove the density of the k-rational points of del Pezzo surfaces of degree 1, we have to search for alternative methods. In this thesis, a result is proven that gives sufficient and necessary conditions for the Zariski density of the rational points on a certain family of del Pezzo surfaces of degree 1.Show less
Bachelor thesis | Griekse en Latijnse taal en cultuur (BA)
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It is known that the density of ancient commentaries is higher in the beginning of the book. I connected this with the mise en page of the Venetus A manuscript, one of the most famous Iliad...Show moreIt is known that the density of ancient commentaries is higher in the beginning of the book. I connected this with the mise en page of the Venetus A manuscript, one of the most famous Iliad manuscripts. The content from different sources is divided over different places on the page. The scribe made his own choices in selecting the content for the manuscript, but was guided by the pedagogical tradition before him, in which the first 12 books of the Iliad were the most important. The amount and content of the scholia is very diverse.Show less
