The explicit construction of orders on surfaces

dc.contributor.advisor Chan, Daniel en_US Bowne-Anderson, Hugo en_US 2022-03-23T18:45:35Z 2022-03-23T18:45:35Z 2011 en_US
dc.description.abstract The study of orders over surfaces is an integral aspect of noncommutative algebraic geometry. Although there is a substantial amount known about orders, relatively few concrete examples have been constructed explicitly. Of those already constructed, most are del Pezzo orders, noncommutative analogues of del Pezzo surfaces, the simplest case. We reintroduce a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira dimension 0. This trick allows us to read off immediately such interesting geometric properties of the order as ramification data and a maximal commutative quotient scheme. We construct maximal orders, noncommutative analogues of normal schemes, on rational surfaces and ruled surfaces. We also use Ogg-Shafarevich theory to construct Azumaya algebras and, more generally, maximal orders on elliptically fibred surfaces. en_US
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.subject.other Numerically Calabi-Yau en_US
dc.subject.other Orders en_US
dc.subject.other Projective surfaces en_US
dc.subject.other Noncommutative en_US
dc.subject.other Algebraic geometry en_US
dc.title The explicit construction of orders on surfaces en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Bowne-Anderson, Hugo
dspace.entity.type Publication en_US
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Bowne-Anderson , Hugo, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Chan, Daniel, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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