Maximal-variation families of general-type varieties over smooth proper DM stacks with generically trivial stabilizers force the log canonical bundle K_X + Delta to be big.
Michigan Math
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Moduli spaces of varieties of general type are naturally of log general type
Maximal-variation families of general-type varieties over smooth proper DM stacks with generically trivial stabilizers force the log canonical bundle K_X + Delta to be big.