Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Moduli of parabolic sheaves on a polarized logarithmic scheme

Author: Mattia Talpo
Journal: Trans. Amer. Math. Soc. 369 (2017), 3483-3545
MSC (2010): Primary 14D20, 14D23
Published electronically: October 12, 2016
MathSciNet review: 3605978
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We generalize the construction of moduli spaces of parabolic
sheaves given by Maruyama and Yokogawa to the case of a projective fine saturated log scheme with a fixed global chart. Furthermore we construct moduli spaces of parabolic sheaves without fixing the weights.

References [Enhancements On Off] (What's this?)

  • [Alp14] Jarod Alper, Adequate moduli spaces and geometrically reductive group schemes, Algebr. Geom. 1 (2014), no. 4, 489-531. MR 3272912,
  • [Alp12] Jarod Alper, Good moduli spaces for Artin stacks, Ann. Inst. Fourier (Grenoble) 63 (2013), no. 6, 2349-2402 (English, with English and French summaries). MR 3237451
  • [Bis97] Indranil Biswas, Parabolic bundles as orbifold bundles, Duke Math. J. 88 (1997), no. 2, 305-325. MR 1455522 (98m:14045),
  • [Bor09] Niels Borne, Sur les représentations du groupe fondamental d'une variété privée d'un diviseur à croisements normaux simples, Indiana Univ. Math. J. 58 (2009), no. 1, 137-180 (French, with English summary). MR 2504408 (2010h:14069),
  • [BV12] Niels Borne and Angelo Vistoli, Parabolic sheaves on logarithmic schemes, Adv. Math. 231 (2012), no. 3-4, 1327-1363. MR 2964607,
  • [FGI$^+$07] Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure, and Angelo Vistoli, Fundamental algebraic geometry: Grothendieck's FGA explained, Mathematical Surveys and Monographs, vol. 123, American Mathematical Society, Providence, RI, 2005. MR 2222646
  • [HL10] Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010. MR 2665168 (2011e:14017)
  • [IS07] Jaya N. N. Iyer and Carlos T. Simpson, A relation between the parabolic Chern characters of the de Rham bundles, Math. Ann. 338 (2007), no. 2, 347-383. MR 2302066 (2008c:14008),
  • [Kat89] Kazuya Kato, Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, pp. 191-224. MR 1463703 (99b:14020)
  • [Lie07] Max Lieblich, Moduli of twisted sheaves, Duke Math. J. 138 (2007), no. 1, 23-118. MR 2309155 (2008d:14018),
  • [Moc06] Takuro Mochizuki, Kobayashi-Hitchin correspondence for tame harmonic bundles and an application, Astérisque 309 (2006), viii+117 (English, with English and French summaries). MR 2310103 (2008f:32029)
  • [MS80] V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), no. 3, 205-239. MR 575939 (81i:14010),
  • [MY92] M. Maruyama and K. Yokogawa, Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), no. 1, 77-99. MR 1162674 (93d:14022),
  • [Nir] Fabio Nironi, Moduli spaces of semistable sheaves on projective Deligne-Mumford stacks,
    Preprint, arXiv:0811.1949.
  • [Ogu] Arthur Ogus, Lectures on logarithmic algebraic geometry,
    TeXed notes,
  • [Ols03] Martin C. Olsson, Logarithmic geometry and algebraic stacks, Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 5, 747-791 (English, with English and French summaries). MR 2032986 (2004k:14018),
  • [OS03] Martin Olsson and Jason Starr, Quot functors for Deligne-Mumford stacks, Comm. Algebra 31 (2003), no. 8, 4069-4096. Special issue in honor of Steven L. Kleiman. MR 2007396 (2004i:14002),
  • [Ses82] C. S. Seshadri, Fibrés vectoriels sur les courbes algébriques, Astérisque, vol. 96, Société Mathématique de France, Paris, 1982 (French). Notes written by J.-M. Drezet from a course at the École Normale Supérieure, June 1980. MR 699278 (85b:14023)
  • [Sta] The Stacks Project authors,
    Stacks Project,
  • [Tal14] Mattia Talpo, Infinite root stacks of logarithmic schemes and moduli of parabolic sheaves,
    Ph.D. thesis, available at, 2014.
  • [TV] M. Talpo and A. Vistoli, Infinite root stacks and quasi-coherent sheaves on logarithmic schemes,
    Preprint, arXiv:1410.1164.
  • [Yok93] Kôji Yokogawa, Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves, J. Math. Kyoto Univ. 33 (1993), no. 2, 451-504. MR 1231753 (94h:14013)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14D20, 14D23

Retrieve articles in all journals with MSC (2010): 14D20, 14D23

Additional Information

Mattia Talpo
Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia V6T 1Z2, Canada

Keywords: Log geometry, parabolic sheaf, moduli of sheaves, root stack
Received by editor(s): January 24, 2015
Received by editor(s) in revised form: May 12, 2015
Published electronically: October 12, 2016
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society