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arXiv · 2312.00887

Some consequences of the $\mu$-constant condition for families of surfaces

Marta Aldasoro Rosales
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Abstract

Let $f : X\to \Delta$ be a $1$-parameter family of $2$-dimensional isolated hypersurface singularities. In this paper, we show that if the Milnor number is constant, then any semistable model, obtained from $f$ after a sufficiently large base change must satisfy non trivial restrictions. Those restrictions are in terms of the dual complex, Hodge structure and numerical invariants of the central fibre.

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Marta Aldasoro Rosales. 2023-12-01. Some consequences of the $\mu$-constant condition for families of surfaces. https://arxiv.org/abs/2312.00887

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