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We study the moduli space of Gieseker semi-stable sheaves on the complexprojective plane supported on sextic curves and having Euler characteristicone. We determine locally free resolutions of length one for all such sheaves.We decompose the moduli space into strata which occur naturally as quotientsmodulo actions of certain algebraic groups. In some cases we give concretegeometric descriptions of the strata.

On the moduli space of semi-stable plane sheaves with Euler characteristic one and supported on sextic curves