The geometrical information encoded by the Euler obstruction of a map

Nivaldo G. Grulha Jr.; Camila Ruiz; Hellen Santana

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arXiv · 2009.06388

The geometrical information encoded by the Euler obstruction of a map

Nivaldo G. Grulha Jr.·Camila Ruiz·Hellen Santana

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Abstract

In this work we investigate the topological information captured by the Euler obstruction of a map, $f:(X,0)\to (\mathbb{C}^{2},0)$, with $(X,0)$ a germ of a complex $d$-equidimensional singular space, with $d > 2$, and its relation with the local Euler obstruction of the coordinate functions and, consequently, with the Brasselet number. Nevertheless, under some technical conditions on the departure variety we relate the Chern number of a special collection related to the map-germ $f$ at the origin with the number of cusps of a generic perturbation of $f$ on a stabilization of $(X,f)$.

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BibTeX RIS

Nivaldo G. Grulha Jr., Camila Ruiz, Hellen Santana. 2020-09-11. The geometrical information encoded by the Euler obstruction of a map. https://arxiv.org/abs/2009.06388

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