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We study the birational complexity of log Calabi-Yau 3-folds. For such a pair (X, B) of index one and coregularity zero, we show that c ₁₈ₑ (X, B) \0, 2, 3\. Further, we prove that (X, B) has a log Calabi-Yau crepant birational model that admits a crepant contraction to (P^3-c, H₀++H₃-₂), where c=c ₁₈ₑ (X, B). To prove this, we give a geometric characterization of standard P¹-links.
Joaquín Moraga (Tue,) studied this question.