@PhdThesis{duepublico_mods_00070523, author = {Gora, Felix}, title = {Local models, Mustafin varieties and semi-stable resolutions}, year = {2019}, month = {Oct}, day = {02}, keywords = {Local models; Mustafin varieties}, abstract = {In this thesis we will analyse singularities of local models. More precisely we will attack the question of existence of semi-stable resolutions. We will discuss an approach mentioned in [Gen00]. In this approach a candidate for a semi-stable resolution was given as the blow-up of a Grassmannian variety in Schubert varieties of its special fiber. Explicit calculations with Sage described in Appendix D show that this approach is not working in general. Starting from the proof of flatness of the local models in [G{\"o}r01], we describe these local models as Mustafinvarieties over Grassmannian varieties. We are combining several results on the structure of Mustafin varieties over projective spaces (cf. [CHSW11],[AL17]) with the Pl{\"u}cker embedding to be able to construct a candidate for a semi-stable resolution of local models. Under some additional assumptions this candidate is generalising the approach suggested by Genestier. Furthermore under the same assumptions the new candidate agrees with the semi-stable resolution constructed in [G{\"o}r04] for small dimensions.}, doi = {10.17185/duepublico/70523}, url = {https://duepublico2.uni-due.de/receive/duepublico_mods_00070523}, url = {https://doi.org/10.17185/duepublico/70523}, file = {:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00070524/Diss_Gora.pdf:PDF}, language = {en} }