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arXiv · 1703.07146

Computing Milnor fiber monodromy for some projective hypersurfaces

Alexandru Dimca·Gabriel Sticlaru
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Abstract

We describe an algorithm computing the monodromy and the pole order filtration on the top Milnor fiber cohomology of hypersurfaces in $\mathbb{P}^n$ whose pole order spectral sequence degenerates at the second page. In the case of hyperplane arrangements and free, locally quasi-homogeneous hypersurfaces, and assuming a key conjecture, this algorithm is much faster than for a hypersurface as above. Our conjecture is supported by the results due to L. Narv\' ez Macarro and M. Saito on the roots of Bernstein-Sato polynomials of such hypersurfaces, by all the examples computed so far, and by one partial result. For hyperplane arrangements coming from reflection groups, a surprising symmetry of their pole order spectra on top cohomology is displayed in our examples. We also improve our previous results in the case of plane curves.

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Alexandru Dimca, Gabriel Sticlaru. 2017-03-21. Computing Milnor fiber monodromy for some projective hypersurfaces. https://arxiv.org/abs/1703.07146

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