Two points of the boundary of toric geometry

Bernard H Teissier (1)

1 IMJ - Institut de Mathématiques de Jussieu

This note presents two observations which have in common that they lie at the boundary of toric geometry. The first one because it concerns the deformation of affine toric varieties into non toric germs in order to understand how to avoid some ramification problems arising in the study of local uniformization in positive characteristic, and the second one because it uses limits of projective systems of equivariant birational maps of toric varieties to study the space of additive preorders on ${\mathbf Z}^r$ for $r\geq 2$.

Mots clés: preorder; Ramification; toric variety

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

Bernard H Teissier. Two points of the boundary of toric geometry. Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, In press. ⟨hal-01835867⟩