# Around the polar degree conjectures

## Singularités et Applications

Lieu:
Kampé de Feriet -- séance commune avec le séminaire Géométrie Algèbrique
Orateur:
Dirk Siersma
Affiliation:
Utrecht University
Dates:
Mardi, 29 Janvier, 2019 - 14:00 - 15:00
Résumé:

Dolgachev (Michigan Math J, 2000) has initiated the study of Cremona polar transformations i.e. birational maps defined by the gradient map of a homogeneous polynomial. He conjectured that the topological degree of depends only on the projective zero locus of , so that it can be called polar degree of , denoted . The hypersurfaces with are called homaloidal; Dolgachev classified the homaloidal plane curves. Dimca and Papadima (Annals of Math 2003) conjectured classification of homaloidal hypersurfaces with isolated singularities was proved by Huh (Duke Math J, 2014). Huh conjectured  the classification of hypersurfaces with isolated singularities and . We formulate in a precise way Huh's conjecture and give its proof.

f:n>n