This analysis introduces birational complexity, focusing on its implications for log Calabi-Yau pairs and their dual complexes.
We introduce the notion of birational complexity of a log Calabi–Yau pair. This invariant measures how far the log Calabi–Yau pair is from being birational to a toric pair. We study fundamental properties of the new invariant, with a particular focus on the geometry of dual complexes.
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Mauri et al. (2025) studied this question.
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