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arXiv · 2105.05743

Polar degree of hypersurfaces with 1-dimensional singularities

Dirk Siersma·Mihai Tibăr
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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.

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Dirk Siersma, Mihai Tibăr. 2021-05-12. Polar degree of hypersurfaces with 1-dimensional singularities. https://doi.org/10.1016/j.topol.2021.107992

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