Faber's conjecture on free divisors and normal crossing singularities
Faber's conjecture on free divisors and normal crossing singularities
Let 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 if there is a subset of codimension at least 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 .
The conjecture asks whether the local normal-crossing condition is determined outside a codimension- subset for free divisors. The preceding proposition establishes only that a reduced free hypersurface with Du Bois singularities is normal crossing in codimension ; 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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