Complements on log canonical fano varieties

Complements on log canonical fano varieties

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Yanning Xu, University of Cambridge
Fine Hall 322

We study anti-canonical systems of log canonical fano varieties. More specifically, we show boundedness of global complements for log canonical fano varieties in dimension less than or equal to 3. This generalises Birkar's recent results about the boundedness of complements for klt fano varieties, which is a key ingredient in the proof of the BAB conjecture. Also we will explain the relationship between the existence of bounded complements for log canonical fano varieties and the index conjecture for log Calabi-Yau varieties. We will also discuss some very recent development on the theory of complements on non fano type varieties in the 3-fold case.