Polar degree and vanishing cycles

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Polar degree and vanishing cycles
 
Siersma, Dirk; Tibăr, Mihai
(2022) Journal of Topology, volume 15, issue 4, pp. 1807 - 1832
(Article)
Abstract
We prove that the polar degree of an arbitrarily singular projective hypersurface can be decomposed as a sum of non-negative numbers which quantify local vanishing cycles of two different types. This yields lower bounds for the polar degree of any singular projective hypersurface.
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Keywords: Taverne, Geometry and Topology
DOI: https://doi.org/10.1112/topo.12260
ISSN: 1753-8416
Publisher: John Wiley and Sons Ltd
Note: Funding Information: The authors thank the Mathematisches Forschungsinstitut Oberwolfach 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. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
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