Orlik's integral diagonalization conjecture for weighted homogeneous monodromy
Assume and that is weighted homogeneous. Let be the matrix of the monodromy operator on with respect to a basis, let be the dimension of this homology group, and let be the identity matrix. Orlik's conjecture. The matrix can be diagonalized over the integers: there exist unimodular matrices and with entries in such that
where divides for . This would give an integral Smith-type decomposition of the monodromy matrix in the weighted homogeneous case; the source provides no resolution of the conjecture.
References
Primary source
Wolfgang Ebeling, “Monodromy”, arXiv:math/0507171 (2005).
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