Polar degree and vanishing cycles

Abstract

We prove that the polar degree of an arbitrarily singular projective hypersurface can be decomposed as a sum of non-negative numbers which represent local vanishing cycles of two different types. This yields lower bounds for the polar degree of any singular projective hypersurface.

accepted for publication by the Journal of Topology

References in corpus (1)

• Polar degree of hypersurfaces with 1-dimensional singularities

Cited by in corpus (2)

• Euclidean distance degree and limit points in a Morsification
• Morse numbers of complex polynomials