Kyoto Journal of Mathematics

Moduli spaces of stable sheaves on Enriques surfaces

Kōta Yoshioka

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Abstract

We study the existence condition of μ-stable sheaves on Enriques surfaces. We also give a different proof of the irreducibility of the moduli spaces of rank 2 stable sheaves.

Article information

Source
Kyoto J. Math., Volume 58, Number 4 (2018), 865-914.

Dates
Received: 9 May 2016
Accepted: 27 December 2016
First available in Project Euclid: 21 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1532138461

Digital Object Identifier
doi:10.1215/21562261-2017-0037

Mathematical Reviews number (MathSciNet)
MR3880241

Zentralblatt MATH identifier
07000590

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14J28: $K3$ surfaces and Enriques surfaces

Keywords
Enriques surfaces stable sheaves moduli

Citation

Yoshioka, Kōta. Moduli spaces of stable sheaves on Enriques surfaces. Kyoto J. Math. 58 (2018), no. 4, 865--914. doi:10.1215/21562261-2017-0037. https://projecteuclid.org/euclid.kjm/1532138461


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References

  • [1] A. B. Altman, A. Iarrobino, and S. L. Kleiman, “Irreducibility of the compactified Jacobian” in Real and Complex Singularities (Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, 1–12.
  • [2] T. Bridgeland, Fourier-Mukai transforms for elliptic surfaces, J. Reine Angew. Math. 498 (1998), 115–133.
  • [3] F. R. Cossec and I. V. Dolgachev, Enriques Surfaces, I, Progr. Math. 76, Birkhäuser, Boston, 1989.
  • [4] D. Gieseker and J. Li, Moduli of high rank vector bundles over surfaces, J. Amer. Math. Soc. 9 (1996), 107–151.
  • [5] M. Hauzer, On moduli spaces of semistable sheaves on Enriques surfaces, Ann. Polon. Math. 99 (2010), 305–321.
  • [6] M. Inaba, On the moduli of stable sheaves on some nonreduced projective schemes, J. Algebraic Geom. 13 (2004), 1–27.
  • [7] H. Kim, Moduli spaces of stable vector bundles on Enriques surfaces, Nagoya Math. J. 150 (1998), 85–94.
  • [8] H. Kim, Stable vector bundles of rank two on Enriques surfaces, J. Korean Math. Soc. 43 (2006), 765–782.
  • [9] K. Kurihara and K. Yoshioka, Holomorphic vector bundles on non-algebraic tori of dimension $2$, Manuscripta Math. 126 (2008), 143–166.
  • [10] J. Li, The first two Betti numbers of the moduli spaces of vector bundles on surfaces, Comm. Anal. Geom. 5 (1997), 625–684.
  • [11] M. Maruyama, Openness of a family of torsion free sheaves, J. Math. Kyoto Univ. 16 (1976), 627–637.
  • [12] M. Maruyama, On boundedness of families of torsion free sheaves, J. Math. Kyoto Univ. 21 (1981), 673–701.
  • [13] K. Matsuki and R. Wentworth, Mumford-Thaddeus principle on the moduli space of vector bundles on an algebraic surface, Internat. J. Math. 8 (1997), 97–148.
  • [14] H. Nuer, A note on the existence of stable vector bundles on Enriques surfaces, Selecta Math. (N.S.) 22 (2016), 1117–1156.
  • [15] K. G. O’Grady, Moduli of vector bundles on projective surfaces: Some basic results, Invent. Math. 123 (1996), 141–207.
  • [16] K. Oguiso and S. Schröer, Enriques manifolds, J. Reine Angew. Math. 661 (2011), 215–235.
  • [17] G. Saccà, Relative compactified Jacobians of linear systems on Enriques surfaces, preprint, arXiv:1210.7519v2 [math.AG].
  • [18] K. Yamada, Singularities and Kodaira dimension of moduli scheme of stable sheaves on Enriques surfaces, Kyoto J. Math. 53 (2013), 145–153.
  • [19] K. Yoshioka, The Betti numbers of the moduli space of stable sheaves of rank $2$ on $\mathbf{P}^{2}$, J. Reine Angew. Math. 453 (1994), 193–220.
  • [20] K. Yoshioka, Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface, Internat. J. Math. 7 (1996), 411–431.
  • [21] K. Yoshioka, A note on the universal family of moduli of stable sheaves, J. Reine Angew. Math. 496 (1998), 149–161.
  • [22] K. Yoshioka, Some examples of Mukai’s reflections on $K3$ surfaces, J. Reine Angew. Math. 515 (1999), 97–123.
  • [23] K. Yoshioka, Irreducibility of moduli spaces of vector bundles on $K3$ surfaces, preprint, arXiv:math/9907001v2 [math.AG].
  • [24] K. Yoshioka, Twisted stability and Fourier-Mukai transform, I, Compos. Math. 138 (2003), 261–288.
  • [25] K. Yoshioka, Twisted stability and Fourier-Mukai transform, II, Manuscripta Math. 110 (2003), 433–465.
  • [26] K. Yoshioka, Stability and the Fourier-Mukai transform, II, Compos. Math. 145 (2009), 112–142.
  • [27] K. Yoshioka, Perverse coherent sheaves and Fourier-Mukai transforms on surfaces, II, Kyoto J. Math. 55 (2015), 365–459.
  • [28] K. Yoshioka, A note on stable sheaves on Enriques surfaces, to appear in Tohoku Math. J., preprint, arXiv:1410.1794v2 [math.AG].