Moduli spaces of rank two ACM bundles on the Segre product of three projective lines
The authors describe the moduli space, denoted by \(\mathcal{M}(c_1,c_2)\), of indecomposable, initialized, ACM semistable bundles of rank 2, with first and second Chern classes denoted respectively by \(c_1\) and \(c_2\), on the Segre embedding of \(\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1\) inside \(\mathbb{P}^7\). Its existence and irreducibility is proved; moreover, the authors describe the moduli space for each possible Chern class. The possible cases for first Chern classes for such bundles where given by the authors in [\textit{G. Casnati} et al., J. Algebra 429, 413--446 (2015; Zbl 1330.14072)]. In the present paper, for each one of the cases, the \(\mu\)-stability of the bundles is studied, and the possibilities for the second Chern classes are given explicitly.
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