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

Published online by Cambridge University Press:  20 November 2018

Oleksandr Iena  and
Alain Leytem
Oleksandr Iena
Affiliation:
University of Luxembourg, Campus Kirchberg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg City, Grand Duchy of Luxembourg. e-mail: [email protected]@uni.lu
Alain Leytem
Affiliation:
University of Luxembourg, Campus Kirchberg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg City, Grand Duchy of Luxembourg. e-mail: [email protected]@uni.lu
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Abstract

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

Keywords

14D20Simpson moduli spacescoherent sheavesvector bundles on curvessingular sheaves
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 522 - 535
Copyright
Copyright © Canadian Mathematical Society 2017

References

[1] Atiyah, M. E. and Macdonald, I. G., Introduction to commutative algebra. Addison-Wesley, Reading, MA, 1969. Google Scholar
[2] Drezet, J.-M., Fibres exceptionnels et varietes de modules de faisceaux semi-stables sur F2 (C). J. Reine Angew. Math. 380(1987), 14–58.Google Scholar
[3] Drezet, J.-M., Varietes de modules alternatives. Ann. Inst. Fourier (Grenoble) 49(1999), no. 1, v-vi, ix, 57–139. Google Scholar
[4] Ellingsrud, G. and Stramme, S. A., On the Chow ring of a geometric quotient. Ann. of Math. (2) 130(1989), 159–187. http://dx.doi.Org/10.2307/1971479 Google Scholar
[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]Google Scholar
[6] Iena, O., Universal plane curve and moduli spaces of 1-dimensional coherent sheaves. Comm. Algebra 43(2015), no. 2, 812–828. http://dx.doi.Org/10.1080/00927872.2013.849265 Google Scholar
[7] Le Potier, J., Faisceaux semi-stables de dimension 1 sur le plan projectif. Rev. Roumaine Math. Pures Appl. 38(1993), no. 7-8, 635–678. Google Scholar
[8] Li, L., Wonderful compactification of an arrangement of subvarieties. Mich. Math. J. 58(2009), no. 2, 535–563. http://dx.doi.Org/10.1307/mmj71250169076 Google Scholar
[9] Maican, M., On two notions of semistability. Pacific J. Math. 234(2008), no. 1, 69–135. http://dx.doi.Org/10.2140/pjm.2008.234.69 Google Scholar
[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, 47–129,1994. Google Scholar
[11] Yuan, Y., Moduli spaces of semistable sheaves of dimension 1 on F . Pure Appl. Math. Q. 10(2014), no. 4, 723–766. http://dx.doi.Org/10.4310/PAMQ.2014.v10.n4.a5 Google Scholar