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arxiv: 1901.03891 · v1 · pith:BH43U4WQnew · submitted 2019-01-12 · 🧮 math.AG

Complements on log canonical Fano varieties

Yanning Xu This is my paper
classification 🧮 math.AG
keywords canonicalcomplementsvarietiesboundednessdimensionfanoprovecalabi-yau
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In this paper, we generalise the theory of complements to log canonical log fano varieties and prove boundedness of complements for them in dimension less than or equal to 3. We also prove some boundedness results for the canonical index of sdlt log Calabi-Yau varieties in dimension 2.

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  1. Failure of the semi log canonical Abundance for compact K\"{a}hler threefolds

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    A counterexample is constructed to the semi-log canonical abundance conjecture for compact Kähler threefolds, while abundance holds for semi-dlt pairs and for slc pairs with positive Kodaira dimension on all normaliza...