Polar degree of hypersurfaces with 1-dimensional singularities

Dirk Siersma*, Mihai Tibăr

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 languageEnglish
Article number107992
Number of pages11
JournalTopology and its Applications
Publication statusPublished - 15 May 2022


  • 1-Dimensional singularities
  • Homaloidal hypersurfaces
  • Polar degree
  • Singular projective hypersurfaces


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