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Recent work on the log minimal model program for the moduli space of curves,as well as past results of Caporaso, Pandharipande, and Simpson motivate aninvestigation of compactifications of the universal moduli space of slopesemi-stable vector bundles over moduli spaces of curves arising in theHassett-Keel program. Our main result is the construction of a universal modulispace of slope semi-stable sheaves which compactifies the moduli space ofvector bundles over the moduli space of pseudo-stable curves.

Universal moduli spaces of vector bundles and the log-minimal model program on the moduli of curves