Skip to main content

On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves

  • Oleksandr Iena (a1) and Alain Leytem (a1)

In the Simpson moduli space M of semi-stable sheaves with Hilbert polynomial dm − 1 on a projective plane we study the closed subvariety M' of sheaves that are not locally free on their support. We show that for d ≥4 , it is a singular subvariety of codimension 2 in M. The blow up of M along M' is interpreted as a (partial) modification of M \ M' by line bundles (on support).

Hide All
[1] Atiyah, M. E. and Macdonald, I. G., Introduction to commutative algebra. Addison-Wesley, Reading, MA, 1969.
[2] Drezet, J.-M., Fibres exceptionnels et varietes de modules de faisceaux semi-stables sur F2 (C). J. Reine Angew. Math. 380(1987), 1458.
[3] Drezet, J.-M., Varietes de modules alternatives. Ann. Inst. Fourier (Grenoble) 49(1999), no. 1, v-vi, ix, 57139.
[4] Ellingsrud, G. and Stramme, S. A., On the Chow ring of a geometric quotient. Ann. of Math. (2) 130(1989), 159187. http://dx.doi.Org/10.2307/1971479
[5] Iena, O., On the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics. arxiv: 13 05.2 400v2 [math .AC]
[6] Iena, O., Universal plane curve and moduli spaces of 1-dimensional coherent sheaves. Comm. Algebra 43(2015), no. 2, 812828. http://dx.doi.Org/10.1080/00927872.2013.849265
[7] Le Potier, J., Faisceaux semi-stables de dimension 1 sur le plan projectif. Rev. Roumaine Math. Pures Appl. 38(1993), no. 7-8, 635678.
[8] Li, L., Wonderful compactification of an arrangement of subvarieties. Mich. Math. J. 58(2009), no. 2, 535563. http://dx.doi.Org/10.1307/mmj71250169076
[9] Maican, M., On two notions of semistability. Pacific J. Math. 234(2008), no. 1, 69135. http://dx.doi.Org/10.2140/pjm.2008.234.69
[10] Simpson, C. T., Moduli of representations of the fundamental group of a smooth projective variety. I. Inst. Hautes Etudes Sci. Publ. Math. (1994), no. 79, 47129,1994.
[11] Yuan, Y., Moduli spaces of semistable sheaves of dimension 1 on F . Pure Appl. Math. Q. 10(2014), no. 4, 723766. http://dx.doi.Org/10.4310/PAMQ.2014.v10.n4.a5
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed