Curves in projective space

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buir.advisorSertöz, Ali Sinan
dc.contributor.authorYıldız, Ali
dc.date.accessioned2016-07-01T10:57:59Z
dc.date.available2016-07-01T10:57:59Z
dc.date.issued2003
dc.departmentDepartment of Mathematicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.description.abstractThis thesis is mainly concerned with classification of nonsingular projective space curves with an emphasis on the degree-genus pairs. In the first chapter, we present basic notions together with a very general notion of an abstract nonsingular curve associated with a function field, which is necessary to understand the problem clearly. Based on Nagata’s work [25], [26], [27], we show that every nonsingular abstract curve can be embedded in some P N and projected to P 3 so that the resulting image is birational to the curve in P N and still nonsingular. As genus is a birational invariant, despite the fact that degree depends on the projective embedding of a curve, curves in P 3 give the most general setting for classification of possible degree-genus pairs. The first notable attempt to classify nonsingular space curves is given in the works of Halphen [11], and Noether [28]. Trying to find valid bounds for the genus of such a curve depending upon its degree, Halphen stated a correct result for these bounds with a wrong claim of construction of such curves with prescribed degree-genus pairs on a cubic surface. The fault in the existence statement of Halphen’s work was corrected later by the works of Gruson, Peskine [9], [10], and Mori [21], which proved the existence of such curves on quartic surfaces. In Chapter 2, we present how the fault appearing in Halphen’s work has been corrected along the lines of Gruson, Peskine, and Mori’s work in addition to some trivial cases such as genus 0, 1, and 2 together with hyperelliptic, and canonical curves.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityYıldız, Alien_US
dc.format.extentvi, 98 leaves, 30 cmen_US
dc.identifier.itemidBILKUTUPB071895
dc.identifier.urihttp://hdl.handle.net/11693/29331
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAbstract curveen_US
dc.subjectmoduli space.en_US
dc.subjectquadric surfaceen_US
dc.subjectquartic surfaceen_US
dc.subjectcubic surfaceen_US
dc.subjectquadric surfaceen_US
dc.subjectdegree-genus pairen_US
dc.subjectdegreeen_US
dc.subjectgenusen_US
dc.subjectprojective embeddingen_US
dc.subjectprojective curveen_US
dc.subjectdiscrete valuation ringen_US
dc.subjecthyperelliptic curveen_US
dc.subjectnonsingular curveen_US
dc.subject.lccQA564 .Y55 2003en_US
dc.subject.lcshGeometry, Algebraic.en_US
dc.titleCurves in projective spaceen_US
dc.typeThesisen_US

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