Tbilisi Mathematical Journal

Rationality and Brauer group of a moduli space of framed bundles

Indranil Biswas, Tomás L. Gómez, and Vicente Muñoz

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We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.

Article information

Tbilisi Math. J., Volume 4 (2011), 29-35.

Received: 25 April 2011
Revised: 3 October 2011
Accepted: 10 October 2011
First available in Project Euclid: 12 June 2018

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Zentralblatt MATH identifier

Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

Brauer group rationality framed bundle stable bundle


Biswas, Indranil; Gómez, Tomás L.; Muñoz, Vicente. Rationality and Brauer group of a moduli space of framed bundles. Tbilisi Math. J. 4 (2011), 29--35. https://projecteuclid.org/euclid.tbilisi/1528768866

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  • V. Balaji, I. Biswas, O. Gabber and D. S. Nagaraj. Brauer obstruction for a universal vector bundle. Comp. Rend. Acad. Sci. Paris 345 (2007), 265–268.
  • I. Biswas, T. Gómez and V. Muñoz Torelli theorem for the moduli space of framed bundles. Math. Proc. Camb. Phil. Soc. 148 (2010), 409–423.
  • H. U. Boden and K. Yokogawa. Rationality of moduli spaces of parabolic bundles. Jour. London Math. Soc. 59 (1999), 461–478.
  • O. Gabber. Some theorems on Azumaya algebras. in: The Brauer Group, pp. 129–209, Lecture Notes in Math., Vol. 844, Springer, Berlin–New York, 1981.
  • N. Hoffmann. Moduli stacks of vector bundles on curves and the King-Schofield rationality proof. in: Cohomological and geometric approaches to rationality problems, pp. 133–148, Progr. Math., 282, Birkhäuser Boston, Inc., Boston, MA, 2010.
  • N. Hoffmann. Rationality and Poincaré families for vector bundles with extra structure on a curve. Int. Math. Res. Not. 2007, no. 3, Art. ID rnm010.
  • D. Huybrechts and M. Lehn. Framed modules and their moduli. Int. Jour. Math. 6 (1995), 297–324.
  • M. Maruyama, Openness of a family of torsion free sheaves. Jour. Math. Kyoto Univ. 16 (1976), 627–637.