Nasr, Amir2023-03-012023-03-012018https://unbscholar.lib.unb.ca/handle/1882/13887In this thesis we work on del Pezzo orders with no worse than canonical singularities. The notion of del Pezzo order is a non-commutative generalization of del Pezzo surfaces. We recall definitions and some facts about orders. We see that orders are a type of non-commutative surfaces. Then we proceed to classify them following the same procedure of classifying del Pezzo (commutative) surfaces. The types of singularities that we work with are terminal and canonical singularities. Once the order has only terminal singularities the classification is very fluent. But when it comes to canonical singularities it needs more work. However, having the classification of terminal orders helps us classify canonical orders. That is because we first resolve canonical singularities to terminal singularities and then we contract them to minimal terminal models.text/xmlix, 125 pageselectronicen-CAhttp://purl.org/coar/access_right/c_abf2doctoral thesis2023-03-01Campbell, EddyIngalls, ColinMathematics and Statistics