On the geography of 3-folds via asymptotic behavior of invariants

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dc.catalogadorpva
dc.contributor.advisorUrzúa Elia, Giancarlo A.
dc.contributor.authorTorres Nova, Yerko Alejandro
dc.contributor.otherPontificia Universidad Católica de Chile. Facultad de Matemáticas
dc.date.accessioned2023-08-21T21:13:47Z
dc.date.available2023-08-21T21:13:47Z
dc.date.issued2023
dc.date.updated2023-08-21T01:47:35Z
dc.descriptionTesis (Doctor en Matemáticas)--Pontificia Universidad Católica de Chile, 2023
dc.description.abstractRoughly speaking, the problem of geography asks for the existence of varieties of general type after we fix some invariants. In dimension 1, where we fix the genus, the geography question is trivial, but already in dimension 2 it becomes a hard problem in general. In higher dimensions, this problem is essentially wide open. In this paper, we focus on geography in dimension 3. We generalize the techniques which compare the geography of surfaces with the geography of arrangements of curves via asymptotic constructions. In dimension 2 this involves resolutions of cyclic quotient singularities and a certain asymptotic behavior of the associated Dedekind sums and continued fractions. We discuss the general situation with emphasis in dimension 3, analyzing the singularities and various resolutions that show up, and proving results about the asymptotic behavior of the invariants we fix.
dc.fechaingreso.objetodigital2023-08-21
dc.format.extent117 páginas
dc.fuente.origenAutoarchivo
dc.identifier.doi10.7764/tesisUC/MAT/74443
dc.identifier.urihttps://doi.org/10.7764/tesisUC/MAT/74443
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/74443
dc.information.autorucFacultad de matemáticas ; Urzúa Elia, Giancarlo A. ; S/I ; 13222
dc.information.autorucFacultad de matemáticas ; Torres Nova, Yerko Alejandro ; S/I ; 1086417
dc.language.isoen
dc.nota.accesoContenido completo
dc.rightsacceso abierto
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleOn the geography of 3-folds via asymptotic behavior of invariantses_ES
dc.typetesis de maestría
sipa.codpersvinculados13222
sipa.codpersvinculados1086417
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