Polar degree of hypersurfaces with 1-dimensional singularities

Dirk Siersma; Mihai Tibăr

doi:10.48550/arXiv.2105.05743

Polar degree of hypersurfaces with 1-dimensional singularities

Research output: Working paper › Preprint › Academic

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.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2105.05743
Publication status	Published - 12 May 2021

Keywords

Mathematics - Algebraic Geometry
32S30
58K60
55R55
32S50

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10.48550/arXiv.2105.05743

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https://arxiv.org/abs/2105.05743

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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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N2 - 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.

AB - 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.

KW - Mathematics - Algebraic Geometry

KW - 32S30

KW - 58K60

KW - 55R55

KW - 32S50

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M3 - Preprint

BT - Polar degree of hypersurfaces with 1-dimensional singularities

PB - arXiv

ER -

Polar degree of hypersurfaces with 1-dimensional singularities

Abstract

Keywords

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