RECERCAT - Articles publicats en revistes (Àlgebra i Geometria)
http://www.recercat.cat:80/handle/2072/48750
www.ub.eduSat, 28 Feb 2015 20:56:36 GMT2015-02-28T20:56:36ZThe Channel Imagehttp://www.recercat.cat:80/bitstream/id/26458/
http://www.recercat.cat:80/handle/2072/48750
Theta-duality on Prym varieties and a Torelli Theorem
http://www.recercat.cat:80/handle/2072/223535
Theta-duality on Prym varieties and a Torelli Theorem
Lahoz Vilalta, Martí; Naranjo del Val, Juan Carlos
Let $\pi : \widetilde C \to C$ be an unramified double covering of irreducible smooth curves and let $P$ be the attached Prym variety. We prove the scheme-theoretic theta-dual equalities in the Prym variety $T(\widetilde C)=V^2$ and $T(V^2)=\widetilde C$, where $V^2$ is the Brill-Noether locus of $P$ associated to $\pi$ considered by Welters. As an application we prove a Torelli theorem analogous to the fact that the symmetric product $D^{(g)}$ of a curve $D$ of genus $g$ determines the curve.
http://www.recercat.cat:80/handle/2072/223535Weight filtration on the cohomology of complex analytic spaces
http://www.recercat.cat:80/handle/2072/246211
Weight filtration on the cohomology of complex analytic spaces
Cirici, Joana; Guillén Santos, Francisco
We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.
http://www.recercat.cat:80/handle/2072/246211$E_{1}$-Formality of complex algebraic varieties
http://www.recercat.cat:80/handle/2072/246047
$E_{1}$-Formality of complex algebraic varieties
Cirici, Joana; Guillén Santos, Francisco
Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.
http://www.recercat.cat:80/handle/2072/246047Sur le théorème locale des cycles invariants
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/2072/210239Monoidal functors, acyclic models and chain operads
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/2072/209635A Cartan-Eilenberg approach to Homotopical Algebra
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/2072/210196On the bicanonical map of irregular varieties
http://www.recercat.cat:80/handle/2072/223534
On the bicanonical map of irregular varieties
Barja Yáñez, Miguel Ángel; Lahoz Vilalta, Martí; Naranjo del Val, Juan Carlos; Pareschi, Giuseppe
From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.
http://www.recercat.cat:80/handle/2072/223534The differentiable chain functor is not homotopy equivalent to the continuous chain functor
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/2072/209909On the bicanonical map of irregular varieties
http://www.recercat.cat:80/handle/2072/223551
On the bicanonical map of irregular varieties
Barja Yáñez, Miguel Ángel; Lahoz Vilalta, Martí; Naranjo del Val, Juan Carlos; Pareschi, Giuseppe
From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.
http://www.recercat.cat:80/handle/2072/223551Arithmetical problems in number fields, abelian varieties and modular forms
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/2072/182325Scrolls and Quartics
http://www.recercat.cat:80/handle/2072/115588
Scrolls and Quartics
Xambó Descamps, Sebastián
http://www.recercat.cat:80/handle/2072/115588On the Gorenstein property of the diagonals of the Rees algebra. (Dedicated to the memory of Fernando Serrano.)
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/2072/115587La proyección plana genérica de una curva alabeada
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/2072/115586On projective varieties of minimal degree
http://www.recercat.cat:80/handle/2072/115585
On projective varieties of minimal degree
Xambó Descamps, Sebastián
http://www.recercat.cat:80/handle/2072/115585Singularidades unidimensionales de una superficie algebraica
http://www.recercat.cat:80/handle/2072/115584
Singularidades unidimensionales de una superficie algebraica
Casas Alvero, Eduardo
http://www.recercat.cat:80/handle/2072/115584Topological computation of local cohomology multiplicities.
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/2072/115583Acerca del género virtual de las superficies algebraicas: Segunda parte
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/2072/115582Filtrations by complete ideals and applications
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/2072/115581K3 surfaces: moduli spaces and Hilbert schemes
http://www.recercat.cat:80/handle/2072/115580
K3 surfaces: moduli spaces and Hilbert schemes
Costa Farràs, Laura
http://www.recercat.cat:80/handle/2072/115580Semi-purity of tempered Deligne cohomology
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/2072/115579Acerca del género virtual de las superficies algebraicas: Primera parte
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/2072/115578Threefolds with nef anticanonical bundles
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/2072/115577El polinomio de Poincaré-Hodge de un producto simétrico de variedades Kählerianas compactas
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/2072/115576Sobre el índice de irregularidad de los números primos
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/2072/115575Graded algebra automorphisms
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/2072/115574A necessary and sufficient condition for a vector field to be Killing
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/2072/115573Sobre el cálculo efectivo del género de las curvas algebraicas
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/2072/115572Sobre inmersiones isométricas de variedades riemannianas en espacios euclídeos
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/2072/115571Galois representations, embedding problems and modular forms
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/2072/115570Localization of nilpotent fibre maps
http://www.recercat.cat:80/handle/2072/115569
Localization of nilpotent fibre maps
Llerena, Irene
http://www.recercat.cat:80/handle/2072/115569