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http://doi.org/10.25358/openscience-9985Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Lehn, Manfred | - |
| dc.contributor.advisor | van Straten, Duco | - |
| dc.contributor.author | Buhr, Lukas | - |
| dc.date.accessioned | 2024-02-15T09:22:22Z | - |
| dc.date.available | 2024-02-15T09:22:22Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.uri | https://openscience.ub.uni-mainz.de/handle/20.500.12030/10003 | - |
| dc.description.abstract | Classical geometric invariant theory as developed by D. Mumford in his book "Geometric Invariant Theory" only applies to actions of a reductive group. G. Bérczi, B. Doran, T. Hawes, and F. Kirwan construct in "Projective Completions of graded unipotent quotients" quotients for non-reductive group actions on projective and irreducible schemes under the assumption that the unipotent radical admits a positive grading. In the first part of this thesis, we study actions of a non-reductive group G on a separated scheme X of finite type over the base field. We formulate a definition for semi-stable and stable points with respect to a pair (K,L) of two G-linearisations and a chosen Levi-factor of G. If the line bundle K is ample, then the locus of semi-stable points admits a good quotient which contains a geometric quotient of the locus of stable points as an open subset. We give a sufficient condition such that the good quotient of the locus of semi-stable points is projective. Further, we prove a Hilbert-Mumford-style criterion to compute the set of semi-stable points. This generalises results by G. Bérczi, B. Doran, T. Hawes and F. Kirwan. In the second part of this thesis, we apply the results of non-reductive geometric invariant theory to construct compactifications of moduli spaces of matrix factorisations of Shamash type. We examine two cases in particular. Let an elliptic quintic curve or a twisted quartic curve be contained in a cubic threefold which is cut out by a homogeneous form f of degree three. We obtain a matrix factorisation of f from the minimal resolution of the homogeneous coordinate ring of the curve over the homogeneous coordinate ring of the ambient projective space with a construction by J. Shamash. For both types of matrix factorisations, we give sufficient numerical conditions on the chosen linearisations (K,L) such that the good quotient of semi-stable generalised matrix factorisations by the action of the automorphism group is projective. This quotient contains a geometric quotient of the locus of stable matrix factorisations as an open subset. | en_GB |
| dc.language.iso | eng | de |
| dc.rights | InCopyright | * |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
| dc.subject.ddc | 510 Mathematik | de_DE |
| dc.subject.ddc | 510 Mathematics | en_GB |
| dc.title | Quotients for non-reductive group actions and applications to moduli spaces of matrix factorisations | en_GB |
| dc.type | Dissertation | de |
| dc.identifier.urn | urn:nbn:de:hebis:77-openscience-24eb48c4-9385-4805-858a-1f96686fa4c77 | - |
| dc.identifier.doi | http://doi.org/10.25358/openscience-9985 | - |
| jgu.type.dinitype | doctoralThesis | en_GB |
| jgu.type.version | Original work | de |
| jgu.type.resource | Text | de |
| jgu.date.accepted | 2024-01-19 | - |
| jgu.description.extent | xiii, 81 Seiten | de |
| jgu.organisation.department | FB 08 Physik, Mathematik u. Informatik | de |
| jgu.organisation.year | 2023 | - |
| jgu.organisation.number | 7940 | - |
| jgu.organisation.name | Johannes Gutenberg-Universität Mainz | - |
| jgu.rights.accessrights | openAccess | - |
| jgu.organisation.place | Mainz | - |
| jgu.subject.ddccode | 510 | de |
| jgu.organisation.ror | https://ror.org/023b0x485 | - |
| Appears in collections: | JGU-Publikationen | |
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| File | Description | Size | Format | ||
|---|---|---|---|---|---|
 | quotients_for_nonreductive_gr-20240125141033764.pdf | 506.47 kB | Adobe PDF | View/Open |