Stability and Fourier-Mukai transforms on higher dimensional elliptic fibrations (Q2396642)

This paper generalizes results from three papers of the second author to the setting of elliptic fibrations with arbitrary dimensional bases. In particular, they check universal closedness for the moduli of semistable objects with respect to a polynomial stability that reduces to PT-stability on threefolds. As a consequence, they prove the openness of this polynomial stability, which allows them to speak of moduli stacks of polynomial stable complexes. After this, they write down a criterion under which some 2-term polynomial stable complexes are mapped to torsion-free semistable sheaves via a Fourier-Mukai transform. As a consequence, they construct an open immersion from a moduli space of complexes to a moduli space of GIeseker stable sheaves on a higher dimensional elliptic fibration.