Mestrado em Matemática
URI Permanente para esta coleção
Nível: Mestrado Acadêmico
Ano de início: 2006
Conceito atual na CAPES: 3
Ato normativo: Homologado pelo CNE ( Port. MEC 609, de 14/03/2019, DOU 18/03/2019)
Periodicidade de seleção: Anual
Área(s) de concentração: Matemática
Url do curso: https://matematica.ufes.br/pt-br/pos-graduacao/PPGMAT/detalhes-do-curso?id=1401
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Navegando Mestrado em Matemática por Autor "Bayer, Valmecir Antonio dos Santos"
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- ItemA estrutura de semigrupos numéricos esparsos(Universidade Federal do Espírito Santo, 2017-01-01) Burock, Katherine Pereira; Oliveira, José Gilvan de; Tizziotti, Guilherme Chaud; Contiero, André Luís; Bayer, Valmecir Antonio dos SantosSparse semigroups will be studied in this dissertation by analyzing their classifications and properties, such as their upper limits for the genus, the interaction between the single and double leaps, the influence of the genus on the leaps, the influence of the parity of the Frobenius number and also the classification of limit sparse semigroups. At the end we will give an introduction to ?-sparse semigroups by analyzing their structure and trying to extend some notions and properties as a natural generalization of the sparse semigroups. For this we will review other published works on the subject, where the main reference used was [1] “On the structure of numerical sparse semigroups and applications”
- ItemCurvas nodais maximais via curvas de Fermat(Universidade Federal do Espírito Santo, 2009-01-01) Profilo, Stanley; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Fantin, SilasWe study the rational projective nodal plane curves in the projective plane P2(C) by using the Fermat curve Fn : Xn+Y n+Zn = 0. We deal with the theory of dual curves in the projective plane and a special type of group action of Zn x Zn on the Fermat curve and its dual to construct, for any positive integer n maior ou igual a 3, a rational nodal plane curve of degree equal to n -1. A rational nodal plane curve is a projective rational plane curve (that is, a genus zero curve) that presents as singularities only nodal points, that is, singularities of multiplicity two with distinct tangents. The basic reference is the paper "On Fermat Curves and Maximal Nodal Curves"by Matsuo OKA published in Michigan Math. Journal, v.53. in 2005.
- ItemFormas modulares e o problema dos números congruentes(Universidade Federal do Espírito Santo, 2015-10-29) Reis, Alexandre Silva dos; Oliveira, José Gilvan de; Conte, Luciane Quoos; Bayer, Valmecir Antonio dos SantosComplex lattices, complex tori and elliptic curves are objects that although having different structures and nature, are equivalent. It is possible by means of a complex lattice to obtain a complex torus and hence, to obtain an elliptic curve; and that “path”’ can also be done in reverse. This connection will be the main object of study in this work, which will also address a careful manner some issues related to it, such as the special linear group, modular forms and modular curves. Finally, as an application of the concepts and tools studied, the congruent numbers problem is considered. This problem besides being closely related to elliptic curves, has a relationship with the famous Birch and Swinnerton-Dyer conjecture, one of the Millennium Problems.
- ItemO Apéry-algoritmo para uma singularidade plana com dois ramos(Universidade Federal do Espírito Santo, 2015-12-18) Vieira, Stéfani Concolato; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Hernandes, Marcelo EscudeiroApery showed, if (??) is a irreductible algebroid plane curve and (?? (1)) is its blowup, then the semigroups ??(??) e ??(?? (1)) associated the curves (??) and (?? (1)) respectively, they can be related. The Apery set is a special generating set of a semigroup with conductor. There is a formula to get the Apery set for ??(?? (1)) from that of ??(??) and vice versa. This does not happen in general for non plane algebroid curves. Through that result of Apery, is possible to show how one can get the semigroup from the multiplicity sequence and vice versa. The main result here is a specie of generalization of results to the case of a plane algebroid curve with two branches, this is, the results of Barucci, Fröberg e D’Anna. We will show how the semigroups ??(??) and ??(?? (1)) are strictly related in the case that (??) has two branches through of Apery set, which it is not finite, but it is a finite union of its components. Furthermore, we will characterize a multiplicity tree of a plane algebroid curve with two branches of purely numerical form
- ItemPontos de Galois de curvas planas projetivas em característica positiva(Universidade Federal do Espírito Santo, 2015-01-01) Lima, Gyslane Aparecida Romano dos Santos de; Bayer, Valmecir Antonio dos Santos; Guimarães, Andréa Gomes; Oliveira, José Gilvan deIn this dissertation we study Galois points in an algebraic non singular plane curve C P2 of degree d 4 in positive characteristic p > 2. The results of H. Yoshihara on the number of inner (respectively outer) Galois points are generalized in this case, under the assumption that d 6 1 modulo p (respectively d 6 0 modulo p). We determine all the number of inner and outer Galois points, in the case that p = d and for quartic curves in three characteristic.
- ItemPontos singulares e pontos de Galois de quárticas planas singulares(Universidade Federal do Espírito Santo, 2011-08-04) Buosi, Carolina Cruz Mendes; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Abdon, MiriamIn this work we study singular plane projective curves of degree four and its Galois points. For this, we fix k, an algebraically closed field of characteristic zero, as the ground field of our discussion. To understand the structure of the function fields of these curves, we use projections: we choose a point P ? P 2 and we project a curve C ? P 2 to a line from P, that is the center of projection. This projection induces an extension field k(C) | k(P 1 ), where k(C) is the rational function field of C. We want to know if there exist intermediate fields in this extension. We analyse two situations: P belongs to the curve C and P doesn’t belong to C
- ItemSemigrupos e o teorema de Gorenstein para singularidades de curvas algébricas planas(Universidade Federal do Espírito Santo, 2013-11-08) Lannes, Andréa Maria Silva; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Salomão, RodrigoThe main goal of this dissertation is to present the Gorenstein Theorem for plane curve singularities. We consider two cases: firstly the local case when the singularity has only one branch and after the semilocal case when the singularity has several branches. In the local case the local equation is given by an irreducible series of k[[X, Y ]] and in the semilocal case it is given by a finite product of irreducible series wich are not pairwise associated. A local equation given by such a power series f is called an algebroid plane curve. The following are objects associated to an algebroid plane curve: The local ring O = O(f), its integral closure O˜ of O in its full ring of fractions and the conductor ideal of O˜ in O. We may say that these data encode all the algebraic / geometric informations of the algebroid plane curve (f). Gorenstein Theorem, that was proved in [Go] by D. Gorenstein states that, in both cases (local or semi-local), the codimension (as k-vector spaces) of the conductor ideal in the ring O is equal to the codimension of the ring O in the ring O˜. This provides us with a certain symmetry which is reflected in the semigroup associated to the algebroid plane curve (f). Thus, we also study the symmetry of semigroups of the natural numbers and relate them to the symmetry of the ring O in the local case.