| dc.date.accessioned | 2020-11-26T13:16:16Z | |
| dc.date.available | 2020-11-26T13:16:16Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | http://hdl.handle.net/10852/81172 | |
| dc.description.abstract | This thesis is a collection of four papers about symmetric and Hermitian determinantal representations of quartic hypersurfaces.
- Paper I classifies rational quartic symmetroids in 3-space.
- Paper II classifies rational quartic spectrahedra in 3-space.
- Paper III finds the maximal dimension for a quartic symmetroid which is singular along a quadric of codimension 1.
- Paper IV gives a bound on the number of isolated essential singularities on a quartic surface with a determinantal representation. A conjecture is formulated about the configurations of isolated essential singularities on quartic surfaces with a Hermitian determinantal representation and a nonempty spectrahedron. | en_US |
| dc.language.iso | en | en_US |
| dc.relation.haspart | Paper I: Helsø, M. ‘Rational quartic symmetroids’. In: Adv. Geom. Vol. 20, no. 1 (2020), pp. 71–89. Included in the thesis. Published version can be found here: https://doi.org/10.1515/advgeom-2018-0037 | |
| dc.relation.haspart | Paper II: Helsø, M., & Ranestad, K. (2021). Rational quartic spectrahedra. Mathematica Scandinavica, 127(1), 79-99. Included in the thesis. Published version can be found here: https://doi.org/10.7146/math.scand.a-121456 | |
| dc.relation.haspart | Paper III: Helsø, M. ‘Maximal dimension of quartic symmetroids with a double quadric of codimension 1’. 2019. Included in the thesis. Pre-print can also be found here: https://arxiv.org/abs/1905.01091 | |
| dc.relation.haspart | Paper IV: Helsø, M. ‘Determinantal quartic surfaces with a definite Hermitian representation’. 2020. Included in the thesis. Pre-print can also be found here: https://arxiv.org/abs/2007.01121 | |
| dc.relation.uri | https://doi.org/10.1515/advgeom-2018-0037 | |
| dc.relation.uri | https://doi.org/10.7146/math.scand.a-121456 | |
| dc.title | Investigations into real determinantal quartic hypersurfaces | en_US |
| dc.type | Doctoral thesis | en_US |
| dc.creator.author | Helsø, Martin | |
| dc.identifier.urn | URN:NBN:no-84257 | |
| dc.type.document | Doktoravhandling | en_US |
| dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/81172/5/PhD-Hels%C3%B8-2020.pdf | |