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.
| Original language | English |
|---|---|
| Pages (from-to) | 1807-1832 |
| Number of pages | 26 |
| Journal | Journal of Topology |
| Volume | 15 |
| Issue number | 4 |
| Early online date | 17 Sept 2022 |
| DOIs | |
| Publication status | Published - Dec 2022 |
Bibliographical 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.
Funding
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).