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Dive into the research topics where Darío Sánchez Gómez is active.

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Featured researches published by Darío Sánchez Gómez.


International Mathematics Research Notices | 2009

Moduli Spaces of Semistable Sheaves on Singular Genus 1 Curves

Daniel Hernández Ruipérez; Ana Martín; Darío Sánchez Gómez; Carlos Tejero Prieto

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure-dimensional sheaves. Using them we establish new identifications between certain Simpson moduli spaces of semistable sheaves on the curve. For rank zero, the moduli spaces are symmetric powers of the curve whilst for a fixed positive rank there are only a finite number of nonisomorphic spaces. We prove similar results for the relative semistable moduli spaces on an arbitrary genus one fibration with no conditions either on the base or on the total space. For a cycle E N of projective lines, we show that the unique degree 0 stable sheaves are the line bundles having degree 0 on every irreducible component and the sheaves supported on one irreducible component. We also prove that the connected component of the moduli space that contains vector bundles of rank r is isomorphic to the rth symmetric product of the rational curve with one node.


arXiv: Algebraic Geometry | 2013

RELATIVE FOURIER-MUKAI TRANSFORMS FOR WEIERSTRASS FIBRATIONS, ABELIAN SCHEMES AND FANO FIBRATIONS

Ana Martín; Darío Sánchez Gómez; Carlos Tejero Prieto

We study the group of relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano or anti-Fano fibrations. For Weierstrass and Fano or anti-Fano fibrations we are able to describe this group completely. For abelian schemes over an arbitrary base we prove that if two of them are relative Fourier-Mukai partners then there is an isometric isomorphism between the fibre products of each of them and its dual abelian scheme. If the base is normal and the slope map is surjective we show that these two conditions are equivalent. Moreover in this situation we completely determine the group of relative Fourier-Mukai transforms and we prove that the number of relative Fourier-Mukai partners of a given abelian scheme over a normal base is finite.


Arkiv för Matematik | 2016

Euler sequence and Koszul complex of a module

Bjorn Andreas; Darío Sánchez Gómez; Fernando Sancho de Salas

We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential p


SPECIAL METRICS AND SUPERSYMMETRY: Proceedings of the Workshop on Geometry and#N#Physics: Special Metrics and Supersymmetry | 2009

Stable Vector Bundles on Calabi‐Yau Threefolds

Björn Andreas; Daniel Hernández Ruipérez; Darío Sánchez Gómez

p


Archive | 2013

Proyecto de innovación docente singalcon - Desarrollo de programas en singular para el aprendizaje del Algebra Conmutativa

Esteban Gómez González; Ana Martín; Darío Sánchez Gómez; Tomás Carlos Tejero Prieto

-forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.


Archive | 2012

Adaptación de materiales docentes y establecimiento de sistemas tutoriales para la docencia de las asignaturas de Álgebra lineal y Geometría del Grado en Físicas

Gloria Serrano Sotelo; Daniel Hernández Serrano; José Ignacio Iglesias Curto; Darío Sánchez Gómez

We construct stable sheaves over K3 fibrations using a relative Fourier‐Mukai transform which describes the sheaves in terms of spectral data. This procedure is similar to the construction for elliptic fibrations, which we also describe. On K3 fibered Calabi‐Yau threefolds, we show that the Fourier‐Mukai transform induces an embedding of the relative Jacobian of spectral line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the Calabi‐Yau manifold.


Archive | 2011

Talleres Computacionales de Algebra Conmutativa

Ana Martín; Esteban Gómez González; José Ignacio Iglesias Curto; Darío Sánchez Gómez


Archive | 2010

Álgebra lineal y geometría I, 2010-11

Gloria Serrano Sotelo; Daniel Hernádez Serrano; Darío Sánchez Gómez


Archive | 2009

Proyecto de innovación docente HALCONES: memoria final

Daniel Hernández Ruipérez; Daniel Hernández Serrano; Ana Martín; Darío Sánchez Gómez


Archive | 2008

ALGORITM-E3s : adaptación de la docencia de la materia "Álgebra Lineal" a las metodologías de aprendizaje por competencias, de acuerdo a la ordenación del Espacio Europeo de Educación Superior, en las titulaciones del rama de conocimiento "Ciencias"

José Ángel Domínguez Pérez; Esteban Gómez González; F. Martín; Tomás Carlos Tejero Prieto; Ana Martín; Gloria Serrano Sotelo; Daniel Hernández Serrano; Darío Sánchez Gómez

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Ana Martín

University of Salamanca

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F. Martín

University of Barcelona

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Bjorn Andreas

Free University of Berlin

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