Cat property conjecture for smooth Fano varieties

Let XX be a nonsingular Fano variety of dimension n2n\geq 2. An effective bQbQ-divisor DD is log canonical in codimension 11 when the pair (X,D)(X,D) is log canonical away from a subset of codimension at least 22. The Cat property is the property defined in the source for Fano varieties.

Cat property conjecture. XX satisfies the Cat property if and only if every effective bQbQ-divisor D\simqKXD\simq-K_X is log canonical in codimension 11.

The conjecture is motivated by examples and results for del Pezzo surfaces, including verification in several low-degree cases. Its status is not resolved in the supplied text.

Sources & referencesView supporting material

Primary source

Jesus Martinez-Garcia, “Dynamic alpha-invariants of del Pezzo surfaces with boundary”, arXiv:1309.1185 (2013).

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