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arXiv · 2401.14951

Signature of the Milnor fiber of parametrized surfaces

R. Giménez Conejero·Gergő Pintér
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Abstract

We compute the signature of the Milnor fiber of certain type of non-isolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show that the signature of the Milnor fiber is a topological invariant for these singularities. The proof combines complex analytic and smooth topological techniques. The main tools are Thom-Mather theory of map germs and the Ekholm-Sz\H{u}cs-Takase-Saeki formula for immersions. We give a table with many examples for which the signature is computed using our formula.

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R. Giménez Conejero, Gergő Pintér. 2024-01-26. Signature of the Milnor fiber of parametrized surfaces. https://arxiv.org/abs/2401.14951

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