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We consider a notion of stability for sheaves, which we call multi-Giesekerstability that depends on several ample polarisations $L_1, \dots, L_N$ and onan additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. Theset of semi stable sheaves admits a projective moduli space $\mathcalM_{\sigma}$. We prove that given a finite collection of parameters $\sigma$,there exists a sheaf- and representation-theoretically defined master space $Y$such that each corresponding moduli space is obtained from $Y$ as a GeometricInvariant Theory (GIT) quotient. In particular, any two such spaces are relatedby a finite number of "Thaddeus-flips". As a corollary, we deduce that any twoGieseker-moduli space of sheaves (with respect to different polarisations $L_1$and $L_2$) are related via a GIT-master space. This confirms an old expectationand generalises results from the surface case to arbitrary dimension.

A Master Space for Moduli Spaces of Gieseker-Stable Sheaves