Polar degree of hypersurfaces with 1-dimensional singularities

Dirk Siersma; Mihai Tibăr

doi:10.1016/j.topol.2021.107992

Polar degree of hypersurfaces with 1-dimensional singularities

Dirk Siersma^*, Mihai Tibăr

^*Corresponding author for this work

Universite de Lille 2

Research output: Contribution to journal › Article › Academic › peer-review

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
Article number	107992
Number of pages	11
Journal	Topology and its Applications
Volume	313
DOIs	https://doi.org/10.1016/j.topol.2021.107992
Publication status	Published - 15 May 2022

Bibliographical note

Funding Information:
The authors thank the Mathematisches Forschungsinstitut Obewolfach for supporting this research project through the Research in Pairs program, and acknowledge the support of the Labex CEMPI grant ( ANR-11-LABX-0007-01 ).

Publisher Copyright:
© 2022 The Authors

Funding

The authors thank the Mathematisches Forschungsinstitut Obewolfach for supporting this research project through the Research in Pairs program, and acknowledge the support of the Labex CEMPI grant ( ANR-11-LABX-0007-01 ).

Keywords

1-Dimensional singularities
Homaloidal hypersurfaces
Polar degree
Singular projective hypersurfaces

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10.1016/j.topol.2021.107992Licence: CC BY

1-s2.0-S0166864121004107-mainFinal published version, 356 KBLicence: CC BY

Cite this

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AU - Tibăr, Mihai

N1 - Funding Information: The authors thank the Mathematisches Forschungsinstitut Obewolfach for supporting this research project through the Research in Pairs program, and acknowledge the support of the Labex CEMPI grant ( ANR-11-LABX-0007-01 ). Publisher Copyright: © 2022 The Authors

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Y1 - 2022/5/15

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 - 1-Dimensional singularities

KW - Homaloidal hypersurfaces

KW - Polar degree

KW - Singular projective hypersurfaces

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JO - Topology and its Applications

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ER -

Polar degree of hypersurfaces with 1-dimensional singularities

Abstract

Bibliographical note

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Keywords

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