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arXiv · 2502.06537

Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities

Bradley Dirks·Laurenţiu Maxim·Sebastián Olano
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Abstract

In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteristic classes for local complete intersections. Our main results describe vanishing properties of these classes in relation to the minimal exponent. As applications, we show how Hirzebruch-Milnor classes of local complete intersections with a projective singular locus can be used to detect higher Du Bois and higher rational singularities.

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Bradley Dirks, Laurenţiu Maxim, Sebastián Olano. 2025-02-10. Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities. https://arxiv.org/abs/2502.06537

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