{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:74147"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:74147","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Real Algebraic Geometry of the Sextic Curves","abstract":"The major part of this thesis revolves around the real algebraic geometry of curves, especially curves of degree six. We use the topological and rigid isotopy classifications of plane sextics to explore the reality of several features associated to each class, such as the bitangents, inflection points, and tensor eigenvectors. We also study the real tensor rank of plane sextics, the construction of quartic surfaces with prescribed topology, and the avoidance locus, which is the locus of all real lines that do not meet a given plane curve. In the case of space sextics, a classical construction relates an important family of these genus 4 curves to the del Pezzo surfaces of degree one. We show that this construction simplifies several problems related to space sextics over the field of real numbers. In particular, we find an example of a space sextic with 120 totally real tritangent planes, which answers a historical problem originating from Arnold Emch in 1928. The last part of this thesis is an algebraic study of a real optimization problem known as Weber problem. We give an explanation and a partial proof for a conjecture on the algebraic degree of the Fermat-Weber point over the field of rational numbers.","abstract_html":"The major part of this thesis revolves around the real algebraic geometry of curves, especially curves of degree six. We use the topological and rigid isotopy classifications of plane sextics to explore the reality of several features associated to each class, such as the bitangents, inflection points, and tensor eigenvectors. We also study the real tensor rank of plane sextics, the construction of quartic surfaces with prescribed topology, and the avoidance locus, which is the locus of all real lines that do not meet a given plane curve. In the case of space sextics, a classical construction relates an important family of these genus 4 curves to the del Pezzo surfaces of degree one. We show that this construction simplifies several problems related to space sextics over the field of real numbers. In particular, we find an example of a space sextic with 120 totally real tritangent planes, which answers a historical problem originating from Arnold Emch in 1928. The last part of this thesis is an algebraic study of a real optimization problem known as Weber problem. We give an explanation and a partial proof for a conjecture on the algebraic degree of the Fermat-Weber point over the field of rational numbers.","abstract_has_math":false,"creators":["Sayyary Namin, Mahsa"],"institution":"Universität Leipzig","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-02-11","date_published":"2021-02-11","updated_at":"2026-07-24T03:56:55Z","subjects":["Real Algebraic Geometry","Computational Algebraic Geometry","Sextic Curves","Avoidance Locus","Tritangent Planes"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Sayyary Namin, Mahsa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Leipzig"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Leipzig"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Real Algebraic Geometry","Computational Algebraic Geometry","Sextic Curves","Avoidance Locus","Tritangent Planes"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The major part of this thesis revolves around the real algebraic geometry of curves, especially curves of degree six. We use the topological and rigid isotopy classifications of plane sextics to explore the reality of several features associated to each class, such as the bitangents, inflection points, and tensor eigenvectors. We also study the real tensor rank of plane sextics, the construction of quartic surfaces with prescribed topology, and the avoidance locus, which is the locus of all real lines that do not meet a given plane curve. In the case of space sextics, a classical construction relates an important family of these genus 4 curves to the del Pezzo surfaces of degree one. We show that this construction simplifies several problems related to space sextics over the field of real numbers. In particular, we find an example of a space sextic with 120 totally real tritangent planes, which answers a historical problem originating from Arnold Emch in 1928. The last part of this thesis is an algebraic study of a real optimization problem known as Weber problem. We give an explanation and a partial proof for a conjecture on the algebraic degree of the Fermat-Weber point over the field of rational numbers."]},{"key":"dc:title","label":"Title","values":["Real Algebraic Geometry of the Sextic Curves"]}]}],"canonical_facts":{"dc:creator":["Sayyary Namin, Mahsa"],"dc:description.abstract":["The major part of this thesis revolves around the real algebraic geometry of curves, especially curves of degree six. We use the topological and rigid isotopy classifications of plane sextics to explore the reality of several features associated to each class, such as the bitangents, inflection points, and tensor eigenvectors. We also study the real tensor rank of plane sextics, the construction of quartic surfaces with prescribed topology, and the avoidance locus, which is the locus of all real lines that do not meet a given plane curve. In the case of space sextics, a classical construction relates an important family of these genus 4 curves to the del Pezzo surfaces of degree one. We show that this construction simplifies several problems related to space sextics over the field of real numbers. In particular, we find an example of a space sextic with 120 totally real tritangent planes, which answers a historical problem originating from Arnold Emch in 1928. The last part of this thesis is an algebraic study of a real optimization problem known as Weber problem. We give an explanation and a partial proof for a conjecture on the algebraic degree of the Fermat-Weber point over the field of rational numbers."],"dc:publisher":["Universitätsbibliothek Leipzig"],"dc:subject":["Real Algebraic Geometry","Computational Algebraic Geometry","Sextic Curves","Avoidance Locus","Tritangent Planes"],"dc:title":["Real Algebraic Geometry of the Sextic Curves"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Leipzig"]},"updated_at":"2026-07-24T03:56:55Z"}