Faber's conjecture on free divisors and normal crossing singularities

Let DD be a free divisor. It has normal crossing singularities if, locally, it is defined by an equation whose irreducible components are smooth and meet transversely. It is normal crossing in codimension 11 if there is a subset of codimension at least 22 outside which it has only normal crossing singularities.

Faber's conjecture. A free divisor has only normal crossing singularities if and only if it is normal crossing in codimension 11.

The conjecture asks whether the local normal-crossing condition is determined outside a codimension-22 subset for free divisors. The preceding proposition establishes only that a reduced free hypersurface with Du Bois singularities is normal crossing in codimension 11; the stated equivalence remains open in the supplied source.

Sources & referencesView supporting material

Primary source

Xia Liao, “K-theoretic defect in Chern class identity for a free divisor”, arXiv:1612.07810 (2016).

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