Formality of Donaldson submanifolds

We introduce the concept of s-formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard Lefschetz property are studied for the symplectic manifolds constructed by Donaldson with asymptotically holomorphic techniques. This study permits us to show an example of a Donaldson symplectic manifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte

Geometric structures on loop and path spaces

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the "almost" independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these spaces are studied.Comment: Final version. To appear in Proceedings of Math. Sci. Indian Academy of Science

Tensorial analisis of the superposed deformation in the easthern border of the Madrid basin

An analysis of Neogene brittle deformation using fault populatíon analysis methods has been carried out between the SW border of the Iberian Range and Altomira Range. Two main paleostress fields have been established: 1) N70E - N120E compression (Altomira paleostress field) ofLate Oligocene - Early Miocene age that induced the formation of the SW border of Iberian Range and Altomira - Pareja thrust belts with reverse and strike-slip faults. 2) N140-N160E compression (Guadarrama paleostress field) of Middle Aragonian - early Pleistocene age that reactivated previous faults with strikeslip movement along the Iberian Range. A superposition of two regional stress fields (Iberian and Guadarrama) is proposed to explain E-W compression that formed Altomira Range. Stress tensorial additions have been realized to check this hypothesis

Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

Strain quantification related to the Berzosa/fault (Spanish Central System)

[Resumen] En relación con la zona de cizalla dúctil de Berzosa Honrubia que actúa durante la segunda fase de deformación Hercínica, se han calculado los elipsoides de deformación finita asociados a la misma. Para el cálculo se usan los métodos de Ramsay (1967), Dunnet (1969), y Fry (1979). Los resultados muestran una variación en el tipo de elipsoide a lo largo de la traza de la zona de cizalla. En los extremos tienen valores K>t, y en la parte central de Kl en la región donde son paralelos.[Abstract] In the ductil shear zone of Berzosa Honrubia, active during the Hercynic second phase, finite strain ellipsoids have been calculated. Methods of Ramsay, Dunnet, and Fry have been used for this calculation. The results show a variation in the strain elipsoid shape through the shear zone trace. The central part h(!s strain ellipsoids with K1. Interpretation of those values is based on the variation in the orientation of the fault cartographic trace and tectonic transport direction. Ellipsoids with K1 are located where the trace and tectonic transport direction are parallel

Population analysis of the late hercynian faulting in the Spanish Central System

[Resumen] En la región comprendida entre Cercedilla, El Espinar y Robleao de Chavela (Sistema Central), se han observado una serie de zonas de cizalla ductiles que cortan a las estructuras Hercínicas anteriores; son de dirección N80-NIIOE y poseen movimientos de tipo normal. Este tipo de régimen distensivo concuerda con tipos deformacionales descritos por otros autores en el Sistema Central Español. En la misma zona están también presentes una serie de diques y fallas frágiles que corresponden a un régimen deformacional inicialmente de tipo distensión uniaxial, según NS-NIOE. Las principales direcciones de fraturación se concretan en dos familias muy próximas (N80E y NIOOE), o en una única familia según N90E. A favor de esta última dirección, yen régimen de tipo extensión uniaxial se emplazan una serie de porfidos graníticos, muy característicos del área estudiada. Debido al temprano emplazamiento de estos diques ya los planos de movimiento deducibles para unos y otros tipos de fallas, pensamos que ambos eventos han de tener una cierta relación temporal. La distensión uniaxial pasa en el tiempo, mediante aumento de las compresiones de dirección N9S-NIOO E, a tectónica de tipo de desgarre. A toda esta evolución deformacional se le denomina «Etapa Malagon». Estos desgarres afectan de una manera dúctil, si bien sin recristalizaciones posteriores, a los diques de porfido granítico, que aun se están emplazando. Posteriormente, y ya dentro de la tectónica netamente de tipo frágil, se produce un régimen deformacional de tipo desgarre, con dirección de compresión NSOE que termina en distensión radial, que hemos denominado «Etapa Hiendelaencina ». En esta fase se emplazan diques de cuarzo y baritina de direcciones N20E' y N80E.[Abstract] In the region between Cercedilla, El Espinar and Robledo de Chavela (Middle Occidental Sector of the Central System) a series of ductile shear zones have been observed that cut to the former Hercynian structures with Nao-NIOO trends and having normal movement. This extensive regime agrees with other previous works. There are, in the same area, a series of dykes and brittle faults that correspond .to a deformational regime with uniaxial extension (initially from N5 to NIO). The main fault trends are Nao and NIOO (or only one with N90 trend). Following this last direction a series of granitic dykes are emplaced. This dyke emplacement and the movement scheme make us think in a certain temporal relation between them. The uniaxial extension changes, with an increase of the compresive axis (N95-NIOO), to a strike-slip fault tectonics. We will call this deformational evolution, «Malagon Phase». Subsequently, and in a clear brittle tectonics, it is produced a deformational regime of strike slip type with a direction of compression of N50E, ending in a radial extension named «Hiendelaencina Phase», with emplacement of quartz and baryte dykes with N20 and Nao trends

Kinematic and dynamic array of the alpine deformations in alto Tajo area (Guadalajara)

The geological macrostructure of Alto Tajo is defined by several N1500E dextral strike-slip faults with related secundary structures. The former set of faults together with others N-S sinistral strike-slip faults delimited areas in transtension and transpession. Four tectonic phases have been detected by means of microstructural analysis: N600E compression; N1500E compression (the main deformation phase). N-S compression, without important structures asociated and a last episode of radial extension.Depto. de Geodinámica, Estratigrafía y PaleontologíaFac. de Ciencias GeológicasFALSEpu

Hodge structures of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. Fix $n\geq 2$, and an integer $d$. A pair $(E,\phi)$ over $X$ consists of an algebraic vector bundle $E$ of rank $n$ and degree $d$ over $X$ and a section $\phi$. There is a concept of stability for pairs which depends on a real parameter $\tau$. Let $M_\tau(n,d)$ be the moduli space of $\tau$-semistable pairs of rank $n$ and degree $d$ over $X$. We prove that the cohomology groups of $M_\tau(n,d)$ are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure $H^1(X)$. This implies a similar result for the moduli spaces of stable vector bundles over $X$.Comment: 23 page