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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
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.lu alain.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.lu alain.leytem@uni.lu
Corresponding

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).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2017

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