Moduli of parabolic sheaves on a polarized logarithmic scheme

Talpo, Mattia

doi:10.1090/tran/6747

Moduli of parabolic sheaves on a polarized logarithmic scheme
HTML articles powered by AMS MathViewer

by Mattia Talpo PDF

Trans. Amer. Math. Soc. 369 (2017), 3483-3545 Request permission

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

Jarod Alper, Adequate moduli spaces and geometrically reductive group schemes, Algebr. Geom. 1 (2014), no. 4, 489–531. MR 3272912, DOI 10.14231/AG-2014-022
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
Indranil Biswas, Parabolic bundles as orbifold bundles, Duke Math. J. 88 (1997), no. 2, 305–325. MR 1455522, DOI 10.1215/S0012-7094-97-08812-8
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, DOI 10.1512/iumj.2009.58.3734
Niels Borne and Angelo Vistoli, Parabolic sheaves on logarithmic schemes, Adv. Math. 231 (2012), no. 3-4, 1327–1363. MR 2964607, DOI 10.1016/j.aim.2012.06.015
Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure, and Angelo Vistoli, Fundamental algebraic geometry, Mathematical Surveys and Monographs, vol. 123, American Mathematical Society, Providence, RI, 2005. Grothendieck’s FGA explained. MR 2222646, DOI 10.1090/surv/123
Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010. MR 2665168, DOI 10.1017/CBO9780511711985
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, DOI 10.1007/s00208-006-0078-7
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
Max Lieblich, Moduli of twisted sheaves, Duke Math. J. 138 (2007), no. 1, 23–118. MR 2309155, DOI 10.1215/S0012-7094-07-13812-2
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
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, DOI 10.1007/BF01420526
M. Maruyama and K. Yokogawa, Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), no. 1, 77–99. MR 1162674, DOI 10.1007/BF01444704
Fabio Nironi, Moduli spaces of semistable sheaves on projective Deligne-Mumford stacks, Preprint, arXiv:0811.1949.
Arthur Ogus, Lectures on logarithmic algebraic geometry, TeXed notes, http://math.berkeley.edu/~ogus/preprints/log_book/logbook.pdf.
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, DOI 10.1016/j.ansens.2002.11.001
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, DOI 10.1081/AGB-120022454
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
The Stacks Project authors, Stacks Project, http://stacks.math.columbia.edu.
Mattia Talpo, Infinite root stacks of logarithmic schemes and moduli of parabolic sheaves, Ph.D. thesis, available at https://www.academia.edu/8683508/Infinite_root_stacks_of_logarithmic_schemes_and_moduli_of_parabolic_sheaves, 2014.
M. Talpo and A. Vistoli, Infinite root stacks and quasi-coherent sheaves on logarithmic schemes, Preprint, arXiv:1410.1164.
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, DOI 10.1215/kjm/1250519269