Séminaire de Géométrie Tropicale
Mercredi 29 mai, 16h15 salle 1525-502
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.