| dc.contributor.advisor | Seppänen, Henrik Jun.-prof. Dr. | |
| dc.contributor.author | Maslovaric, Marcel | |
| dc.date.accessioned | 2018-06-26T08:46:07Z | |
| dc.date.available | 2018-06-26T08:46:07Z | |
| dc.date.issued | 2018-06-26 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E430-8 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6925 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Variational Geometric Invariant Theory and Moduli of Quiver Sheaves | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Seppänen, Henrik Jun.-prof. Dr. | |
| dc.date.examination | 2018-01-18 | |
| dc.description.abstracteng | We are concerned with two applications of GIT.
First, we prove that a geometric GIT quotient of an a ne variety X =
Spec(A) by a reductive group G, where A is an almost factorial domain, is a
Mori dream space, regardless of the codimension of the unstable locus. This
includes an explicit description of the Picard number, the pseudoe ective
cone, and the Mori chambers in terms of GIT.
We apply the results to quiver moduli to show that they are Mori dream
spaces if the quiver contains no oriented cycles, and if stability and semistability
coincide. We give a formula for the Picard number in quiver terms.
As a second application, we prove that geometric quotients of Mori dream
spaces are Mori dream spaces as well, which again includes a description
of the Picard number and the Mori chambers. Some examples are given to
illustrate the results.
The second instance where we use GIT, is the construction and variation of
moduli spaces of quiver sheaves.
To that end, we generalize the notion of multi{Gieseker semistability for
coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for
a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves
using a functorial method that realizes these as subschemes of moduli spaces
of representations of a twisted quiver, depending on Q, with relations. We
also show the projectivity of the moduli space in the case when Q has no
oriented cycles. Further, we construct moduli spaces of quiver sheaves which
satisfy a given set of relations as closed subvarieties.
Finally, we investigate the parameter dependence of the moduli. | de |
| dc.contributor.coReferee | Pidstrygach, Viktor Prof. Dr. | |
| dc.contributor.thirdReferee | Greb, Daniel Prof. Dr. | |
| dc.subject.eng | Algebraic Geometry | de |
| dc.subject.eng | Geometric Invariant Theory | de |
| dc.subject.eng | Birational geometry | de |
| dc.subject.eng | Moduli spaces | de |
| dc.subject.eng | Sheaf theory | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E430-8-0 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 1025240448 | |