# Around the polar degree conjectures

## Géométrie Algébrique

Lieu:
Salle Kampé de Fériet M2
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 grad $f: \mathbb{P}^n - - > \mathbb{P}^n$ defined by the gradient map of a homogeneous polynomial. The hypersurfaces with $\texttt{pol}(V)=1$ are called homaloidal; Dolgachev classified the homaloidal plane curves. Dimca and Papadima (Ann. Math 2003) conjectural classification of homaloidal hypersurfaces with isolated singularities was proved more recently by Huh (Duke Math J, 2014). Huh himself conjectured the list of hypersurfaces with isolated singularities and $\texttt{pol}(V)=2$. We formulate in a precise way Huh's conjecture and give its proof.