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Geometria complexa generalizada e tópicos relacionados / Generalized complex geometry and related topicsAlves, Leonardo Soriani, 1991- 27 August 2018 (has links)
Orientadores: Luiz Antonio Barrera San Martin, Lino Anderson da Silva Grama / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T10:27:44Z (GMT). No. of bitstreams: 1
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Previous issue date: 2015 / Resumo: Estudamos geometria complexa generalizada, que tem como casos particulares as geometrias complexa e simplética. Começamos com os seus fundamentos algébricos num espaço vetorial e transportamos essas noções para variedades. Estudamos o colchete de Courant na soma direta dos fibrados tangente e cotangente de uma variedade, que é essencial para definir a integrabilidade das estruturas complexas generalizadas. Verificamos que em nilvariedades de dimensão 6 sempre existe estrutura complexa generalizada invariante à esquerda, ainda que algumas delas não admitam estrutura complexa ou simplética. Estudamos duas noções de T-dualidade e suas relações com geometria complexa generalizada. Por fim recapitulamos a simetria do espelho para curvas elípticas e obtemos uma manifestação de simetria do espelho através de geometria complexa generalizada / Abstract: We study generalized complex geometry, which encompasses complex and symplectic geometry as particular cases. We begin with the algebraic basics on a vector space and then we transport these concepts to manifolds. We study the Courant bracket on the direct sum of tangent and cotangent bundles of a manifold, which is essential to define the integrability of the generalized complex structures. We check that on every $6$ dimensional nilmanifolds there is a left invariant generalized complex structure, even though some of them do not admit complex or symplectic structure. We study two notions of T-dualidade and its relations to generalized complex geometry. We recall mirror symmetry for elliptic curves and derive a manifestation of mirror symmetry from generalized complex geometry / Mestrado / Matematica / Mestre em Matemática
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Cohomology of the moduli space of curves of genus three with level two structureBergvall, Olof January 2014 (has links)
In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately. / Målet med denna uppsats är att undersöka modulirummet M3[2] av kurvor av genus 3 med symplektisk nivå 2 struktur. Mer specifikt vill vi hitta informationom kohomologin av detta rum. För att uppnå detta delar vi först upp M[2] i en disjunkt union av två naturliga delrum, Q[2] och H3[2], och räknar därefter punkterna av dessa rum S7- respektive S8-ekvivariant.
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Distinguished representations : the generalized injectivity conjecture and symplectic models for unitary groups / Autour des représentations distinguées : la conjecture d'injectivité généralisée et modèles symplectiques pour les groupes unitairesDijols, Sarah 06 July 2018 (has links)
Soit $G$ un groupe connexe quasi-déployé défini sur un corps non-Archimédien de caractéristique nulle. On suppose que l'on se donne un sous-groupe parabolique standard de décomposition de Levi $P=MU$ ainsi qu'une représentation irréductible tempérée $\tau$ de $M$. Soit $\nu$ un élement dans le dual de l'algèbre de Lie de la composante déployée de $M$; on le choisit dans la chambre de Weyl positive. La représentation induite $I_P^G(\tau_{\nu})$ est appelée module standard. Quand la représentation $\tau$ est générique (pour un caractère non-dégénéré de $U$), i.e a un modèle de Whittaker, le module standard $I_P^G(\tau_{\nu})$ est également générique.Casselman et Shahidi ont conjecturé que l'unique sous-quotient générique apparaissait nécessairement comme sous-représentation dans le module standard $I_P^G(\tau_{\nu})$. Ceci a été démontrée dans le cas des groupes classiques $SO(2n+1), Sp(2n)$, et $SO(2n)$ quand $P$ est un sous-groupe parabolique maximal de $G$, par Hanzer en 2010.Dans notre travail, nous formulons et étudions ce problème dans le contexte plus général d'un groupe connexe quasi-déployé tel que les composantes irréductibles de $\Sigma_{\sigma}$ sont de type $A,B,C$ ou $D$.Dans la deuxième partie de cette thèse (en commun avec D.Prasad), nous prouvons d'abord qu'il n'existe pas de representation cuspidale du groupe quasi-déployé $\U_{2n}(F)$ qui soit distinguée par son sous-groupe $\Sp_{2n}(F)$ pour $F$ un corps local non-Archimédien. Nous prouvons ensuite le théorème équivalent pour un corps global: il n'existe pas de représentation cuspidale de $\U_{2n}(\A_k)$ qui ait une période symplectique non nulle pour $k$ un corps de nombres ou corps de fonctions. / Let $G$ be a quasi-split connected reductive group over a non-Archimedean local field $F$ of characteristic zero. We assume we are given a standard parabolic subgroup $P$ with Levi decomposition $P=MU$ as well as an irreducible, tempered representation $\tau$ of $M$. Let now $\nu$ be an element in the dual of the real Lie algebra of the split component of $M$; we take it in the positive Weyl chamber. The induced representation $I_P^G(\tau_{\nu})$ is called a standard module. When the representation $\tau$ is generic (for a non-degenerate character of $U$), i.e. has a Whittaker model, the standard module $I_P^G(\tau_{\nu})$ is also generic. Casselman and Shahidi have conjectured that the unique irreducible generic subquotient of a standard module $I_P^G(\tau_{\nu})$ is necessarily a subrepresentation. This conjecture known as the Generalized Injectivity Conjecture was proved for the classical groups $SO(2n+1), Sp(2n)$, and $SO(2n)$ for $P$ a maximal parabolic subgroup, by Hanzer in 2010.In our work, we formulate and study this problem for any quasi-split connected reductive group such that the irreducible components of $\Sigma_{\sigma}$ are of type $A,B,C$ or $D$. In the second part of this thesis (joint work with D.Prasad), we prove that there are no cuspidal representations of the quasi-split unitary groups $\U_{2n}(F)$ distinguished by $\Sp_{2n}(F)$ for $F$ a non-archimedean local field. We also prove the corresponding global theorem that there are no cuspidal representations of $\U_{2n}(\A_k)$ with nonzero period integral on $\Sp_{2n}(k) \backslash \Sp_{2n}(\A_k)$ for $k$ any number field or a function field.
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Geometry and Arithmetic of the LLSvS VarietyGiovenzana, Franco 01 April 2021 (has links)
This thesis concerns the hyperkähler eightfold constructed by Lehn, Lehn, Sorgen, and van Straten, built from twisted cubics on a cubic fourfold. We study its period, its birational properties and we describe some geometric features.
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Cohomology of the moduli space of curves of genus three with level two structureBergvall, Olof January 2014 (has links)
In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately. / Målet med denna uppsats är att undersöka modulirummet M3[2] av kurvor av genus 3 med symplektisk nivå 2 struktur. Mer specifikt vill vi hitta informationom kohomologin av detta rum. För att uppnå detta delar vi först upp M[2] i en disjunkt union av två naturliga delrum, Q[2] och H3[2], och räknar därefter punkterna av dessa rum S7- respektive S8-ekvivariant.
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Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions / 複素射影平面上のシンプレクティック束及び直交束のモジュライ空間とK理論ネクラソフ分配関数Choy, Jaeyoo 23 March 2015 (has links)
京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第12910号 / 論理博第1546号 / 新制||理||1590(附属図書館) / 32120 / ソウル大学大学院数学科 / (主査)教授 中島 啓, 教授 小野 薫, 教授 向井 茂 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM
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On an algebro-geometric realization of the cohomology ring of conical symplectic resolutions / 錐的シンプレクティック特異点解消のコホモロジー環の代数幾何学的実現についてHikita, Tatsuyuki 25 May 2015 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19166号 / 理博第4106号 / 新制||理||1591(附属図書館) / 32158 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 加藤 周, 教授 並河 良典, 教授 雪江 明彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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On smoothness of minimal models of quotient singularities by finite subgroups of SLn(C) / SLn(C)の有限部分群による商特異点の極小モデルの非特異性についてYamagishi, Ryo 26 March 2018 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20884号 / 理博第4336号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 並河 良典, 教授 雪江 明彦, 教授 森脇 淳 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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Unique K3 Surfaces with Purely Non-Symplectic Automorphism: Insights from Weighted Projective SpaceUnique K3 Surfaces with Purely Non-Symplectic Automorphism:\\Insights from Weighted Projective SpaceMelville, Elizabeth 22 April 2024 (has links) (PDF)
K3 surfaces have garnered attention across various fields, from optics and dynamics to high energy physics, making them a subject of extensive study for many decades. Recent work by mathematicians, including Brandhorst [1], has focused on non-symplectic automorphisms, aiming to categorize K3 surfaces that admit such automorphisms. Brandhorst made a list of unique K3 surfaces with purely non-symplectic automorphisms and established specific criteria for a K3 surface to be isomorphic to one on his list. This thesis aims to provide an alternative representation of select K3 surfaces from Brandhorst's list. While Brandhorst predominantly characterizes these surfaces as elliptic K3 surfaces, we offer a description of these surfaces as hypersurfaces in weighted projective space. Our approach involves verifying the criteria established by Brandhorst, thereby establishing an isomorphism between the surfaces in question. Through this study, we contribute to the understanding of K3 surfaces and their automorphisms while also demonstrating the correspondence between different spaces and methodologies for analyzing K3 surfaces. This work lays the groundwork for further investigations into K3 surfaces with purely non-symplectic automorphisms, paving the way for deeper insights into their structural properties and geometric intricacies.
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Strong Gelfand Pairs of Some Finite GroupsMarrow, Joseph E. 25 July 2024 (has links) (PDF)
Strong Gelfand pairs describe a relation between a group and a subgroup, using a relation between inner products of their characters. We find all strong Gelfand pairs of the dihedral and dicyclic groups, and several of the sporadic groups. We provide some results for the strong Gelfand pairs of the affine linear groups, in addition to the exceptional classical groups $\mathrm{Sp}_4(q)$ for $q$ a power of $2$.
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