Séminaire de Géométrie Tropicale

Institut Mathématiques de Jussieu ,
Université Pierre et Marie Curie, Paris 6
UMR CNRS 7586




Mercredi 29 mai, 16h15 salle 1525-502



Mounir Nisse (Texas A&M)

Higher convexity of (co)amoebas complements and their homology

Résumé :
I will strengthen Henriques's result about the higher convexity of amoeba complements when the underlying variety is a complete intersection, and extend it to coamoebas complements in the general case (i.e., without the assumption of complete intersection). Also, if the codimension of our variety is $r$, and the complement of its amoeba is $\mathscr{A}^c$, then I define a map from the integer homology group $H_{r-1}(\mathscr{A}^c,\mathbb{Z})$ to $H^r((\mathbb{C}^*)^n, \mathbb{Z})$ generalizing the order map of the hypersurface case. I will describe the relation between the homology of amoeba complement and the variety itself, and give a lower bound of the dimension of $H_{n+r-1}((\mathbb{C}^*)^n\setminus V)$ in terms of the dimension of $H_{r-1}(\mathscr{A}^c)$. This is a joint work with Frank Sottile.