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Polar degree of hypersurfaces with 1-dimensional singularities

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1_s2.0_S0166864121004107_main.pdf (356.13 KB)

Publication date

2022-05-15

Authors

Siersma, DirkISNI 0000000116400912
Tibăr, Mihai

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DOI

https://doi.org/10.1016/j.topol.2021.107992

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Article

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Utrecht University Repository
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Abstract

We prove a formula for the polar degree of projective hypersurfaces in terms of the Milnor data of the singularities, extending to 1-dimensional singularities the Dimca-Papadima result for isolated singularities. We discuss the semi-continuity of the polar degree in deformations, and we classify the homaloidal cubic surfaces with 1-dimensional singular locus. Some open questions are pointed out along the way.

Keywords

1-Dimensional singularities, Homaloidal hypersurfaces, Polar degree, Singular projective hypersurfaces, Geometry and Topology

Citation

Siersma, D & Tibăr, M 2022, 'Polar degree of hypersurfaces with 1-dimensional singularities', Topology and its Applications, vol. 313, 107992. https://doi.org/10.1016/j.topol.2021.107992

URI

http://hdl.handle.net/1874/420944