English

Polar degree of hypersurfaces with 1-dimensional singularities

Algebraic Geometry 2022-05-18 v1

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

Cite

@article{arxiv.2105.05743,
  title  = {Polar degree of hypersurfaces with 1-dimensional singularities},
  author = {Dirk Siersma and Mihai Tibăr},
  journal= {arXiv preprint arXiv:2105.05743},
  year   = {2022}
}