"however , by expanding this result to dlt pairs we give the different proof of the abundance theorem for log canonical pairs in the case where [MATH] from and : [ = theorem ] let [MATH] be a normal projective variety and [MATH] an effective [MATH] - divisor .",rb4125"however , by expanding this result to dlt pairs we give the different proof of the abundance theorem for log canonical pairs in the case [MATH] as shown by and : [ = theorem ] let [MATH] be a normal projective variety and [MATH] an effective [MATH] - divisor ."

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"assume that the isotropy subalgebra of [MATH] in [MATH] be distinct from [MATH] , and take a parabolic subgroup [MATH] of [MATH] whose levi factor is the isotropy subgroup of [MATH] in [MATH] .","under the assumption that the isotropy subalgebra of [MATH] in [MATH] is drb 3343 2017istinct from [MATH] , take a parabolic subgroup [MATH] of [MATH] whose levi factor is the isotropy subgroup of [MATH] in [MATH] , and let [MATH] be the open covering of the flag variety [MATH] indexed by [MATH] ( see e : open_covering_of_the_flag_variety for details ) ."

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