dc.contributor.author
Portakal, Irem
dc.date.accessioned
2018-09-26T11:37:21Z
dc.date.available
2018-09-26T11:37:21Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/23007
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-805
dc.description.abstract
One can associate to a bipartite graph a so-called edge ring and its spectrum is an affine normal toric variety. We first characterize the faces of the (edge) cone associated to this toric variety in terms of certain independent sets of the bipartite graph. Then, we give first examples of rigid toric varieties associated to bipartite graphs. We show their rigidity combinatorially, to wit, purely in terms of graphs. In the next chapters, we determine the two and three-dimensional faces of the edge cone. With this information, we show that these toric varieties are smooth in codimension two and the non-simplicial three-dimensional faces are generated by exactly four extremal rays. In the latter case, we get non rigid toric varieties. Lastly, we study torus actions on matrix Schubert varieties. In the toric case, we present a classification for their rigidity.
en
dc.format.extent
ix, 88 Seiten
de
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
de
dc.subject
toric variety
en
dc.subject
first order deformation
en
dc.subject
bipartite graph
en
dc.subject.ddc
500 Natural sciences and mathematics::510 Mathematics::512 Algebra and number theory
de
dc.title
Rigidity of toric varieties associated to bipartite graphs
de
dc.contributor.gender
female
de
dc.contributor.firstReferee
Altmann, Klaus
dc.contributor.furtherReferee
Christophersen, Jan Arthur
dc.date.accepted
2018-04-27
dc.identifier.urn
urn:nbn:de:kobv:188-refubium-23007-2
refubium.affiliation
Mathematik und Informatik
de
dcterms.accessRights.dnb
free
de
dcterms.accessRights.openaire
open access
