The Generalized Torelli Problem through the geometry of the Gauss map

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dc.catalogadorgjm
dc.contributor.advisorAuffarth, Robert
dc.contributor.authorRahausen Rodríguez, Sebastián Andrés
dc.contributor.otherPontificia Universidad Católica de Chile. Facultad de Matemáticas
dc.date.accessioned2024-07-23T15:10:54Z
dc.date.available2024-07-23T15:10:54Z
dc.date.issued2024
dc.date.updated2024-07-19T22:28:09Z
dc.descriptionTesis (Doctor en Matemática)--Pontificia Universidad Católica de Chile, 2024.
dc.description.abstractGiven a non-hyperelliptic curve C of genus g and 1<n<g-1, in this work we prove that the generic fiber of the Gauss map on W_n has one element and we characterize its multiple locus. Assuming that C doesn't have a linear system of dimension k+1 and degree n+k+1, for 0<k<n<g-1, we solve the problem of reconstructing each linear system of dimension k and degree n+k, and the dual hypersurface of the image of its associated morphism, through information encoded in the Gauss map. For this purpose we introduce the notion of (n+k)-intersection loci and we study their dimensions. In the hyperelliptic case we prove that the image of the Gauss map is a union of sets whose closures are birational to their complete linear systems of dimension k and degree n+k, for each 0<k<n+1<g+1, and that these also contain a copy of the dual hypersurface of the image of its associated morphism. From the case k=n we deduce that the closure of the image of the Gauss map is birational to the n-dimensional projective space.We also prove the existence of points in W_n such that their images on the Kummer variety of their Jacobian aren't in general position, i.e., they lie on a multisecant. For this purpose we use the Gunning multisecant formula. We then study some relations between these multisecant points and the Gauss map on W_n, in both cases non-hyperelliptic and hyperelliptic.
dc.fechaingreso.objetodigital2024-07-23
dc.format.extentiv, 73 páginas
dc.fuente.origenAutoarchivo
dc.identifier.doi10.7764/tesisUC/MAT/87208
dc.identifier.urihttps://doi.org/10.7764/tesisUC/MAT/87208
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/87208
dc.information.autorucFacultad de Matemáticas; Auffarth, Robert; S/I; 162672
dc.information.autorucFacultad de Matemáticas; Rahausen Rodríguez, Sebastián Andrés; S/I; 1092442
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleThe Generalized Torelli Problem through the geometry of the Gauss map
dc.typetesis doctoral
sipa.codpersvinculados162672
sipa.codpersvinculados1092442
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