Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-04-30T11:32:48.102Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli of Space Sheaves with Hilbert Polynomial 4m + 1

Published online by Cambridge University Press:  20 November 2018

Mario Maican
Mario Maican*
Affiliation:
Institute of Mathematics of the Romanian Academy, Calea Grivitei 21, Bucharest 010702, Romania, e-mail: maican@imar.ro
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

Keywords

14D2014D22moduli of sheavessemi-stable sheaves
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 328 - 345
Copyright
Copyright © Canadian Mathematical Society 2018

References

[1] Ballico, E. and Huh, S., Stable sheaves on a smooth quadric surface with linear Hubert bipolynomials. The Scientific World Journal (2014), Article ID 346126.Google Scholar
[2] Chen, D. and Nollet, S., Detaching embeddedpoints. Algebra Number Theory 6(2012), 731–756.http://dx.doi.Org/10.2140/ant.2012.6.731 Google Scholar
[3] Choi, J. and Chung, K. The geometry ofthe moduli Space of one-dimensional sheaves. Sei. China Math. 58(2015), 487–500.http://dx.doi.Org/1 0.1007/s11425-014-4889-9 Google Scholar
[4] Choi, J. and Chung, K., Moduli Spaces of α-stablepairs and wall-crossing on ℙ2. J. Math. Soc. Japan 68(2016), 685–709.http://dx.doi.org/10.2969/jmsj706820685 Google Scholar
[5] Choi, J., Chung, K., and Maican, M., Moduli of sheaves supported on quartic Space curves. Michigan Math. J. 65(2016), 637–671.http://dx.doi.org/10.1307/mmj71472066152 Google Scholar
[6] Choi, J. and Maican, M., Torus action on the moduli Spaces oftorsion plane sheaves of multiplicity four. J. Geom. Phy. 83(2014), 18–35.http://dx.doi.Org/10.1016/j.geomphys.2014.05.005 Google Scholar
[7] Drézet, J.-M. and Maican, M., On the geometry ofthe moduli Spaces of semi-stable sheaves supported on plane quartics. Geom. Dedicata 152(2011), 17–49.http://dx.doi.Org/10.1007/s10711-010-9544-1 Google Scholar
[8] Freiermuth, H.-G. and Trautmann, G., On the moduli scheme of stable sheaves supported on eubie Space curves. Amer. J. Math. 126(2004), 363–393.http://dx.doi.Org/10.1353/ajm.2004.0013 Google Scholar
[9] Huybrechts, D. and Lehn, M., The geometry of moduli Spaces of sheaves. Aspects of Mathematics, E31, Vieweg, Braunschweig, 1997.http://dx.doi.Org/10.1007/978-3-663-11624-0 Google Scholar
[10] Iena, O., On the Singular 1-dimensional planar sheaves supported on quartics. Rend. Istit. Mat. Univ. Trieste 48(2016), 565–586.Google Scholar
[11] Le Potier, J., Faisceaux semi-stables de dimension 1 sur le plan projeetif Rev. Roumaine Math. Pures Appl. 38(1993), 635–678.Google Scholar
[12] Maican, M., A duality resultfor moduli Spaces of semistable sheaves supported on projeetive curves. Rend. Semin. Mat. Univ. Padova 123(2010), 55–68.http://dx.doi.Org/10.4171/RSMUP/123-3 Google Scholar
[13] Maican, M., The homology groups ofeertain moduli Spaces of plane sheaves. Internat. J. Math. 24(2013), Article ID 1350098.http://dx.doi.Org/10.1142/S01 291 67X13500985 Google Scholar
[14] Maican, M., On the homology ofthe moduli Space of plane sheaves with Hilbert polynomial 5m + 3. Bull. Sei. Math. 139(2015), 1–32. http://dx.doi.Org/10.1016/j.bulsci.2O14.08.001 Google Scholar
[15] Popov, V. and Vinberg, E., Invariant theory. In: Algebraic Geometry IV, Encyclopedia of Mathematical Sciences, 55, Springer Verlag, Berlin, 1994.http://dx.doi.org/10.1007/978-3-662-03073-8 Google Scholar
[16] Shafarevich, I., Basic algebraic geometry. I. Second ed., Springer-Verlag, Berlin, Heidelberg, 1994.Google Scholar
[17] Vainsencher, I. and Avritzer, D., Compactifying the Space of elliptic quartic curves. In: Complex projeetive geometry, (Trieste, 1989), London Math. Soc. Lecture Note Ser., 179, Cambridge University Press, Cambridge, 47-58.Google Scholar