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You searched for subject:(Albanese varieties). Showing records 1 – 3 of 3 total matches.

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Universitat Politècnica de Catalunya

1. Lahoz Vilalta, Marti. Theta-duality in abelian varieties and the bicanonical map of irregular varieties.

Degree: 2010, Universitat Politècnica de Catalunya

El primer objectiu d'aquesta tesi és contribuir a l'estudi de les varietats abelianes principalment polaritzades (vapp), especialment als problemes de Schottky i Torelli. Les vapp admeten una teoria de dualitat anàloga a la dualitat dels espais projectius, on el paper que juguen els hiperplans de l'espai projectiu és substituït pels divisors que representen la polarització principal. Així doncs, donada una subvarietat Y d'una vapp, podem definir el seu thetadual T(Y) com el conjunt dels divisors que representen la polarització principal i contenen aquesta subvarietat. Aquest conjunt admet una estructura esquemàtica natural (tal i com la defineixen Pareschi i Popa). Les varietats Jacobianes i de Prym són exemples clàssics de vapp construïdes a partir de corbes. A més, són interessants perquè certes propietats de les corbes involucrades es veuen reflectides en elles o en algunes subvarietats especials. Per exemple, en el cas de les Jacobianes tenim els llocs de BrillNoether Wd ( W1 correspon a la corba d'AbelJacobi) i en el cas de les Pryms tenim la corba d'AbelPrym C. Al capítol III de la tesi s'estudia l'estructura esquemàtica del thetadual dels llocs de BrillNoether Wd i de la corba d'AbelPrym. En el primer cas, es reobté amb uns altres mètodes, el resultat de Pareschi i Popa T(Wd)= Wgd1. En el cas de la corba d'AbelPrym C, s'obté que T(C)=V², onV² és el segon lloc de PrymBrillNoether amb l'estructura esquemàtica definida per Welters. Pareschi i Popa han demostrat un resultat anàleg per les vapp al Lemma de Castelnuovo pels espais projectius. És a dir, si (A,Θ) és una vapp de dimensió g, aleshores g+2 punts en posició general respecte Θ, però en posició especial respecte 2Θ, han d'estar continguts en una corba de grau minimal a A, i.e. una corba d'AbelJacobi. En particular, s'obté un resultat de Schottky ja que A ha de ser una Jacobiana i un resultat de Torelli, ja que la corba és la intersecció de tots els divisors de |2Θ| que contenen els g+2 punts. Al capítol IV, tal i com Eisenbud i Harris van fer en el cas projectiu, s'estén aquest resultat a esquemes finits possiblement no reduïts. El segon objectiu d'aquesta tesi és contribuir a l'estudi de les varietats de tipus general. Pràcticament per definició, les aplicacions pluricanòniques són essencials pel seu estudi. Un dels problemes principals de l'àrea és donar condicions geomètriques o numèriques per assegurar que la mèsima aplicació pluricanònica (per m baix) indueix una equivalència biracional amb la imatge. La classificació de les superfícies que tenen l'aplicació bicanònica no biracional ha atret l'atenció de molts geòmetres algebraics. Al capítol V, es dóna un criteri numèric suficient per assegurar la biracionalitat de l'aplicació bicanònica de les varietats irregulars de dimensió arbitrària. També es demostra que si X és una varietat primitiva, aleshores només admet fibracions molt especials a altres varietats irregulars. Per aquestes varietats s'obté que és equivalent que X sigui biracional a un divisor Θ en una… Advisors/Committee Members: Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística, [email protected] (authoremail), false (authoremailshow), Barja Yáñez, Miguel Ángel (director), Naranjo del Val, Juan Carlos (codirector), true (authorsendemail).

Subjects/Keywords: Fourier-mukai transform; Abelian varieties; Varieties of maximal albanese dimension; Bicanonical map; Finite subschemes on abelian varieties; Schottky problem; Birational geometry; Prym varieties; Jacobian varieties; 51

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APA (6th Edition):

Lahoz Vilalta, M. (2010). Theta-duality in abelian varieties and the bicanonical map of irregular varieties. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/77898

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Lahoz Vilalta, Marti. “Theta-duality in abelian varieties and the bicanonical map of irregular varieties.” 2010. Thesis, Universitat Politècnica de Catalunya. Accessed July 09, 2020. http://hdl.handle.net/10803/77898.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Lahoz Vilalta, Marti. “Theta-duality in abelian varieties and the bicanonical map of irregular varieties.” 2010. Web. 09 Jul 2020.

Vancouver:

Lahoz Vilalta M. Theta-duality in abelian varieties and the bicanonical map of irregular varieties. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2010. [cited 2020 Jul 09]. Available from: http://hdl.handle.net/10803/77898.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lahoz Vilalta M. Theta-duality in abelian varieties and the bicanonical map of irregular varieties. [Thesis]. Universitat Politècnica de Catalunya; 2010. Available from: http://hdl.handle.net/10803/77898

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Universitat Autònoma de Barcelona

2. Giné Vázquez, Iago. Albanese varieties of non-Archimedean uniformized varieties.

Degree: Departament de Matemàtiques, 2017, Universitat Autònoma de Barcelona

In this PhD thesis, we give a conjectural construction of the Albanese variety of a non-Archimedean uniformized variety by means of looking at a metrical structure contained in the last one and called its skeleton (which is, essentially, a tropical curve). In order to do that we make a parallel (real, tropical) construction on the skeleton, which becomes the skeleton of the conjectural Albanese we were seeking for, we rise this to an analytic construction over the given variety and we use that its skeleton is the quotient of a certain locally finite subbuilding of a Bruhat-Tits building, which appears also as the skeleton of the uniformizing variety. Later, we relate the harmonic cochains on the buildings with the harmonic measures on the ends as a key step in the proof that one gets the Albanese variety. The thesis has two main parts. One is devoted to describe with complete generality this construction in dimension 1, while in the second we study the structure of the Bruhat-Tits building and we make a construction that we expect it is the Albanese variety, under the assumption that the ground field has a discrete valuation. We start by study the Jacobian of a graph, in the chapter 1 without more structure, in the chapter 2 a metric graph. Our work, together with others, shows that our description of the Jacobian of a metric graph in terms of integration on the ends of the universal covering metric tree extends in some way the (discrete) Jacobian of a graph without metric structure. Here we introduce harmonic cochains on the trees and harmonic measures on the ends, and we prove that they are isomorphic, as an important step to the main result. In the chapter 3 we develope the theory of Mumford curves and their Jacobians in the setting of Berkovich geometry, we relate them with their skeletons by means of the retraction map and we introduce the multiplicative integrals. Then, we extend to our general hypotheses several known results about them in particular cases (like for a local ground field) with those new tools, and we use the results on the Jacobian of a metric graph applied to the corresponding skeleton to get that the construction we do with multiplicative integrals and harmonic measures is an abelian variety. After that, we prove that it is the Jacobian by means of the theory of theta functions, developed from the new perspective of Berkovich geometry using tropical functions. In the chapter 4 we adapt this construction to higher dimension, giving a natural candidate to be the Albanese variety of a non-Archimedean uniformized variety as it was built by Mustafin as a generalization of Mumford curves. In order to do it, we extend the notion of Schottky group to any dimension following the work of Mustafin, and we study deeply the structure of the Bruhat-Tits buildings over a complete field with a discrete valuation. Then, we restrict to dimension 2 to define the harmonic cochains over certain chamber subcomplexes, and we prove that they are isomorphic to the harmonic measures over a certain compact set of… Advisors/Committee Members: [email protected] (authoremail), true (authoremailshow), Xarles Ribas, Francesc Xavier (director), true (authorsendemail).

Subjects/Keywords: Varietats d'Albanese; Variedades de Albanese; Albanese varieties; Geometria analitica de Berkovich; Geometria analitica de Berkovich; Berkovich analytic geometry; Edificis de Bruhat-Tits; Edificios de Bruhat-Tits; Bruhat-Tits buildings; Ciències Experimentals; 514

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Giné Vázquez, I. (2017). Albanese varieties of non-Archimedean uniformized varieties. (Thesis). Universitat Autònoma de Barcelona. Retrieved from http://hdl.handle.net/10803/405530

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Giné Vázquez, Iago. “Albanese varieties of non-Archimedean uniformized varieties.” 2017. Thesis, Universitat Autònoma de Barcelona. Accessed July 09, 2020. http://hdl.handle.net/10803/405530.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Giné Vázquez, Iago. “Albanese varieties of non-Archimedean uniformized varieties.” 2017. Web. 09 Jul 2020.

Vancouver:

Giné Vázquez I. Albanese varieties of non-Archimedean uniformized varieties. [Internet] [Thesis]. Universitat Autònoma de Barcelona; 2017. [cited 2020 Jul 09]. Available from: http://hdl.handle.net/10803/405530.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Giné Vázquez I. Albanese varieties of non-Archimedean uniformized varieties. [Thesis]. Universitat Autònoma de Barcelona; 2017. Available from: http://hdl.handle.net/10803/405530

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Pham, Tuan D. On the Picard Varieties of Surfaces with Equivalent Derived Categories.

Degree: 2012, University of Illinois – Chicago

It was shown recently by Popa and Schnell that the irregularities of two smooth projective varieties with equivalent bounded derived categories of coherent sheaves are equal. They conjectured that the Picard varieties of smooth projective varieties with equivalent derived categories are derived equivalent. This thesis investigates this conjecture for the case of smooth projective surfaces. More specifically, we showed that the Picard varieties of derived equivalent surfaces are in fact derived equivalent with the possible exception of the case of properly elliptic surfaces with constant j-invariant. In that case, we also provide an analysis of the Picard variety. In addition, we give a statement about the automorphism groups of derived equivalent surfaces. Advisors/Committee Members: Popa, Mihnea (advisor), Ein, Lawrence (committee member), Coskun, Izzet (committee member), Schnell, Christian (committee member), Arapura, Donu (committee member).

Subjects/Keywords: algebraic geometry; derived categories; Picard varieties; automorphism groups; Albanese varieties; Fourier-Mukai transforms

…picture of Picard varieties, the groups Aut0 and the Albanese dimensions for derived equivalent… …SUMMARY The study of derived categories as invariants of algebraic varieties has… …algebraic varieties are preserved by derived equivalences. Only until recently, Popa and Schnell… …preserved under derived equivalences. They also conjectured that the Picard varieties of derived… …equivalent varieties are derived equivalent. This conjecture clearly holds in the case of curves… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Pham, T. D. (2012). On the Picard Varieties of Surfaces with Equivalent Derived Categories. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9623

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Pham, Tuan D. “On the Picard Varieties of Surfaces with Equivalent Derived Categories.” 2012. Thesis, University of Illinois – Chicago. Accessed July 09, 2020. http://hdl.handle.net/10027/9623.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Pham, Tuan D. “On the Picard Varieties of Surfaces with Equivalent Derived Categories.” 2012. Web. 09 Jul 2020.

Vancouver:

Pham TD. On the Picard Varieties of Surfaces with Equivalent Derived Categories. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2020 Jul 09]. Available from: http://hdl.handle.net/10027/9623.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pham TD. On the Picard Varieties of Surfaces with Equivalent Derived Categories. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/9623

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.