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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.46 no.2 Bogotá jul./dez. 2012

 

Fourier-Mukai Transform for Twisted Derived Categories of Surfaces

La transformada de Fourier-Mukai para categorías derivadas torcidas de superficies

HERMES MARTÍNEZ1

1Universidad Sergio Arboleda, Bogotá, Colombia. Email: hermes.martinez@usa.edu.co


Abstract

In this paper we study the classification of surfaces under twisted derived categories.

Key words: Twisted derived categories, Brauer groups, Moduli spaces.


2000 Mathematics Subject Classification: 16E35, 16K50, 37P45.

Resumen

En este artículo estudiamos la clasificación de superficies bajo las categorías derivadas torcidas.

Palabras clave: Categorías derivadas torcidas, grupos de Brauer, espacios moduli.


Texto completo disponible en PDF


References

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[2] A. Bondal and D. Orlov, 'Reconstruction of a Variety from the Derived Category and Groups of Autoequivalences', Comp. Math. 125, (2001), 327-344.         [ Links ]

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[4] T. Bridgeland and A. Maciocia, 'Complex Surfaces with Equivalent Derived Categories', Math. Z. 236, 4 (2001), 677-697.         [ Links ]

[5] A. Caldararu, Derived Categories of Twisted Sheaves on Calabi-Yau Manifolds, PhD thesis, Cornell University,         [ Links ] 2000.

[6] A. Canonaco and P. Stellari, 'Twisted Fourier-Mukai Functors', Adv. Math. 212, 2 (2007), 484-503.         [ Links ]

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[8] R. Donagi and T. Pantev, Torus Fibrations, Gerbes, and Duality, Vol. 193 of Memoirs of the American Mathematical Society Series, Amer Mathematical Society,         [ Links ] 2008.

[9] R. Friedman and J. Morgan, Smooth Four-Manifolds and Complex Surfaces, Vol. 27 of Ergebnisse Math. Grengeb., Springer-Verlag, Berlin, Germany,         [ Links ] 1994.

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[11] D. Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, UK,         [ Links ] 2006.

[12] Y. Kawamata, 'D-Equivalence and K-Equivalence', J. Diff. Geom. 61, 1 (2002), 147-171.         [ Links ]

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[14] S. Mukai, 'Duality between D(X) and D(\widehatX) with its Applications to Picard Sheaves', Nagoya Math. J, 81 (1981), 153-175.         [ Links ]

[15] D. Orlov, 'Derived Categories of Coherent Sheaves and Equivalences between them', Russian Math. Surveys 58, 3 (2003), 511-591.         [ Links ]

[16] A. Polishschuk, Abelian Varieties, Theta Functions and the Fourier Transform, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK,         [ Links ] 2003.


(Recibido en mayo de 2012. Aceptado en noviembre de 2012)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv46n2a06,
    AUTHOR  = {Martínez, Hermes},
    TITLE   = {{Fourier-Mukai Transform for Twisted Derived Categories of Surfaces}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2012},
    volume  = {46},
    number  = {2},
    pages   = {205--228}
}