On Huh's conjectures for the polar degree

TL;DR

This paper proves a refined version of June Huh's conjecture, confirming the complete list of projective hypersurfaces with isolated singularities and a polar degree of 2, advancing understanding in algebraic geometry.

Contribution

It provides a rigorous proof of Huh's conjecture and verifies the conjectural classification of specific hypersurfaces with given singularity and polar degree.

Findings

Confirmed Huh's conjectural list of hypersurfaces with polar degree 2.

Proved a precise version of Huh's general conjecture.

Validated the classification of hypersurfaces with isolated singularities and polar degree 2.

Abstract

We prove a precise version of a general conjecture on the polar degree stated by June Huh. We confirm Huh's conjectural list of all projective hypersurfaces with isolated singularities and polar degree equal to 2.