Global (log) canonical threshold of d-sheeted covers of M-dimensional projective space of index 1 is 1 for almost all families (d≥4) under quadratic singularity and regularity assumptions, implying birational rigidity of Fano-Mori fibre spaces with base dimension bounded quadratically by fibre dim.
V., Birationally rigid Fano fibrations
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Canonical and log canonical thresholds of multiple projective spaces
Global (log) canonical threshold of d-sheeted covers of M-dimensional projective space of index 1 is 1 for almost all families (d≥4) under quadratic singularity and regularity assumptions, implying birational rigidity of Fano-Mori fibre spaces with base dimension bounded quadratically by fibre dim.