Illinois Journal of Mathematics

On the moduli spaces of semi-stable plane sheaves of dimension one and multiplicity five

Mario Maican

Full-text: Open access


We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases, we also find geometric descriptions of these sheaves by means of extensions. We give natural stratifications for their moduli spaces and we describe the strata as certain quotients modulo linear algebraic groups. In most cases, we give concrete descriptions of these quotients as fibre bundles.

Article information

Illinois J. Math., Volume 55, Number 4 (2011), 1467-1532.

First available in Project Euclid: 12 July 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14D22: Fine and coarse moduli spaces


Maican, Mario. On the moduli spaces of semi-stable plane sheaves of dimension one and multiplicity five. Illinois J. Math. 55 (2011), no. 4, 1467--1532. doi:10.1215/ijm/1373636694.

Export citation


  • J.-M. Drézet, Fibrés exceptionnels et variétés de modules de faisceaux semi-stables sur $\P_2(\C)$, J. Reine Angew. Math. 380 (1987), 14–58.
  • J.-M. Drézet, Variétés de modules alternatives, Ann. Inst. Fourier 49 (1999), 57–139.
  • J.-M. Drézet, Espaces abstraits de morphismes et mutations, J. Reine Angew. Math. 518 (2000), 41–93.
  • J.-M. Drézet and M. Maican, On the geometry of the moduli spaces of semi-stable sheaves supported on plane quartics, Geom. Dedicata 152 (2011), 17–49.
  • J.-M. Drézet and G. Trautmann, Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups, Ann. Inst. Fourier 53 (2003), 107–192.
  • D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics, vol. E31, Vieweg, Braunschweig, 1997.
  • A. D. King, Moduli of representations of finite dimensional algebras, Q. J. Math. 45 (1994), 515–530.
  • J. Le Potier, Faisceaux semi-stables de dimension 1 sur le plan projectif, Rev. Roumaine Math. Pures Appl. 38 (1993), 635–678.
  • M. Maican, On two notions of semistability, Pacific J. Math. 234 (2008), 69–135.
  • M. Maican, A duality result for moduli spaces of semistable sheaves supported on projective curves, Rend. Semin. Mat. Univ. Padova 123 (2010), 55–68.