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COMPACTIFICATIONS OF CLUSTER VARIETIES ASSOCIATED TO ROOT SYSTEMS

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dc.contributor.advisorPaul Hacking
dc.contributor.authorXIE, FEIFEI
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27T18:43:21.000
dc.date.accessioned2024-04-26T15:37:29Z
dc.date.available2024-04-26T15:37:29Z
dc.date.submittedFebruary
dc.date.submitted2020
dc.description.abstractIn this thesis we identify certain cluster varieties with the complement of a union of closures of hypertori in a toric variety. We prove the existence of a compactification $Z$ of the Fock--Goncharov $\mathcal{X}$-cluster variety for a root system $\Phi$ satisfying some conditions, and study the geometric properties of $Z$. We give a relation of the cluster variety to the toric variety for the fan of Weyl chambers and use a modular interpretation of $X(A_n)$ to give another compactification of the $\mathcal{X}$-cluster variety for the root system $A_n$.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/15991744
dc.identifier.orcidhttps://orcid.org/0000-0001-6861-4242
dc.identifier.urihttps://hdl.handle.net/20.500.14394/18137
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=2912&context=dissertations_2&unstamped=1
dc.source.statuspublished
dc.subjectcluster variety
dc.subjectroot system
dc.subjecttoric variety
dc.subjectAlgebraic Geometry
dc.titleCOMPACTIFICATIONS OF CLUSTER VARIETIES ASSOCIATED TO ROOT SYSTEMS
dc.typeopenaccess
dc.typearticle
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:xiefeifei1989@gmail.com|institution:University of Massachusetts Amherst|XIE, FEIFEI
digcom.identifierdissertations_2/1871
digcom.identifier.contextkey15991744
digcom.identifier.submissionpathdissertations_2/1871
dspace.entity.typePublication
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