A big real divisor is an actual positive real combination of big Cartier divisors. Equivalently it is real linearly equivalent, or numerically equivalent, to an ample real divisor plus an effective real divisor. The rational approximation of an ample-plus-effective real divisor and Kodaira's lemma connect these formulations. Fujino's notes on big real divisors give the definition also for nonnormal varieties; bigness under finite normalization relates it to section growth.
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