http://www.recercat.cat:80/handle/2072/48750 www.ub.edu Sun, 19 May 2013 04:36:23 GMT 2013-05-19T04:36:23Z http://www.recercat.cat:80/bitstream/id/26458/ http://www.recercat.cat:80/handle/2072/48750 http://www.recercat.cat:80/handle/2072/210239 Sur le théorème locale des cycles invariants Guillén Santos, Francisco; Navarro, Vicenç (Navarro Aznar) Si on considère une famille de variétés projectives complexes non singulières, c"est un fait aujourd'hui bien connu que les possibles variétés singulières vers lesquelles peut dégénerer cette famille doivent vérifier certaines contraintes, parmi lesquelles une importante relation entre la cohomologie de la fibre singulière, la cohomologie de la fibre générique et la monodromie de la famille, qui est precise par le théorème local des cycles invariants prouvé par Clemens, Deligne et Steenbrink ([1], [4], [13]) : tous les cocycles de la fibre générique qui sont invariants par la monodromie autour d¡une fibre singulière proviennent par spécialisation de la cohomologie de cette fibre singulière. http://www.recercat.cat:80/handle/2072/210239 http://www.recercat.cat:80/handle/2072/210196 A Cartan-Eilenberg approach to Homotopical Algebra Guillén Santos, Francisco; Navarro, Vicenç (Navarro Aznar); Pascual, Pere (Pascual i Gainza); Roig Martí, Agustí In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem. http://www.recercat.cat:80/handle/2072/210196 http://www.recercat.cat:80/handle/2072/209909 The differentiable chain functor is not homotopy equivalent to the continuous chain functor Guillén Santos, Francisco; Navarro, Vicenç (Navarro Aznar); Pascual, Pere (Pascual i Gainza); Roig Martí, Agustí Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence. http://www.recercat.cat:80/handle/2072/209909 http://www.recercat.cat:80/handle/2072/209635 Monoidal functors, acyclic models and chain operads Guillén Santos, Francisco; Navarro, Vicenç (Navarro Aznar); Pascual, Pere (Pascual i Gainza); Roig Martí, Agustí We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras. http://www.recercat.cat:80/handle/2072/209635 http://www.recercat.cat:80/handle/2072/182325 Arithmetical problems in number fields, abelian varieties and modular forms Bayer i Isant, Pilar, 1946-; Vila, Núria (Vila i Oliva); Arenas, A. (Àngela), 1955-; Crespo Vicente, Teresa; Travesa i Grau, Artur Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research. http://www.recercat.cat:80/handle/2072/182325 http://www.recercat.cat:80/handle/2072/115588 Scrolls and Quartics Xambó Descamps, Sebastián http://www.recercat.cat:80/handle/2072/115588 http://www.recercat.cat:80/handle/2072/115587 On the Gorenstein property of the diagonals of the Rees algebra. (Dedicated to the memory of Fernando Serrano.) Lavila Vidal, Olga; Zarzuela, Santiago http://www.recercat.cat:80/handle/2072/115587 http://www.recercat.cat:80/handle/2072/115586 La proyección plana genérica de una curva alabeada Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115586 http://www.recercat.cat:80/handle/2072/115585 On projective varieties of minimal degree Xambó Descamps, Sebastián http://www.recercat.cat:80/handle/2072/115585 http://www.recercat.cat:80/handle/2072/115584 Singularidades unidimensionales de una superficie algebraica Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115584 http://www.recercat.cat:80/handle/2072/115583 Topological computation of local cohomology multiplicities. García López, Ricardo, 1962-; Sabbah, Claude We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link. http://www.recercat.cat:80/handle/2072/115583 http://www.recercat.cat:80/handle/2072/115582 Acerca del género virtual de las superficies algebraicas: Segunda parte Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115582 http://www.recercat.cat:80/handle/2072/115581 Filtrations by complete ideals and applications Casas Alvero, Eduardo Infinitely near base points and Enriques' unloading procedure are used to construct filtrations by complete ideals of C{x, y}. It follows a procedure for getting generators of the integral closure of an ideal. http://www.recercat.cat:80/handle/2072/115581 http://www.recercat.cat:80/handle/2072/115580 K3 surfaces: moduli spaces and Hilbert schemes Costa Farràs, Laura http://www.recercat.cat:80/handle/2072/115580 http://www.recercat.cat:80/handle/2072/115579 Semi-purity of tempered Deligne cohomology Burgos Gil, José I. In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties. http://www.recercat.cat:80/handle/2072/115579 http://www.recercat.cat:80/handle/2072/115578 Acerca del género virtual de las superficies algebraicas: Primera parte Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115578 http://www.recercat.cat:80/handle/2072/115577 Threefolds with nef anticanonical bundles Peternell, Th. (Thomas), 1954-; Serrano, Fernando In this paper we study the global structure of projective threefolds X whose anticanonical bundle K is nef. http://www.recercat.cat:80/handle/2072/115577 http://www.recercat.cat:80/handle/2072/115576 El polinomio de Poincaré-Hodge de un producto simétrico de variedades Kählerianas compactas Burillo, Josep http://www.recercat.cat:80/handle/2072/115576 http://www.recercat.cat:80/handle/2072/115575 Sobre el índice de irregularidad de los números primos Bayer i Isant, Pilar, 1946- http://www.recercat.cat:80/handle/2072/115575 http://www.recercat.cat:80/handle/2072/115574 Graded algebra automorphisms Vela del Olmo, Ma. Montserrat We consider the Clifford algebra C(q) of a regular quadratic space (V, q) over a field K with its structure of Z/2Z-graded K-algebra. We give a characterization of the group of graded automorphisms of C(q). In the last section we introduce the Z/nZ-graded algebras and we study as well as the group of graded automorphisms for some of them. http://www.recercat.cat:80/handle/2072/115574 http://www.recercat.cat:80/handle/2072/115573 A necessary and sufficient condition for a vector field to be Killing Currás Bosch, Carlos http://www.recercat.cat:80/handle/2072/115573 http://www.recercat.cat:80/handle/2072/115572 Sobre el cálculo efectivo del género de las curvas algebraicas Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115572 http://www.recercat.cat:80/handle/2072/115571 Sobre inmersiones isométricas de variedades riemannianas en espacios euclídeos Currás Bosch, Carlos http://www.recercat.cat:80/handle/2072/115571 http://www.recercat.cat:80/handle/2072/115570 Galois representations, embedding problems and modular forms Crespo Vicente, Teresa To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms. http://www.recercat.cat:80/handle/2072/115570 http://www.recercat.cat:80/handle/2072/115569 Localization of nilpotent fibre maps Llerena, Irene http://www.recercat.cat:80/handle/2072/115569 http://www.recercat.cat:80/handle/2072/115568 On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam) D'Andrea, Carlos, 1973-; Chipalkatti, Jaydeep http://www.recercat.cat:80/handle/2072/115568 http://www.recercat.cat:80/handle/2072/115567 Singularidades de una hoja de superficie algebraica a partir de su serie de Puiseux Casas Alvero, Eduardo http://www.recercat.cat:80/handle/2072/115567 http://www.recercat.cat:80/handle/2072/115566 Estructuras circulares y su orientación Pascual Xufré, Griselda, 1926-2001 http://www.recercat.cat:80/handle/2072/115566 http://www.recercat.cat:80/handle/2072/115565 On the motive of a quotient variety Baño Rollin, Sebastian del; Navarro, Vicenç (Navarro Aznar) We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive. http://www.recercat.cat:80/handle/2072/115565 http://www.recercat.cat:80/handle/2072/115564 Bounds on multisecant lines Nollet, Scott The purpose of this paper is two fold. First, we give an upper bound on the orderof a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we givean explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine standardlinking theorem. These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems. http://www.recercat.cat:80/handle/2072/115564