Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-5c569c448b-t6r6x Total loading time: 0.203 Render date: 2022-07-02T06:38:53.464Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true
  • English
Canadian Mathematical Bulletin Canadian Mathematical Bulletin

Article contents

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: oleksandr.iena@uni.lualain.leytem@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: oleksandr.iena@uni.lualain.leytem@uni.lu
Get access Rights & Permissions[Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. CrossRefGoogle 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 CrossRefGoogle 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 CrossRefGoogle 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 CrossRefGoogle 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 CrossRefGoogle 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 CrossRefGoogle Scholar
1
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

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

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *