4 papers
Lipschitz saturation of toric singularities in any dimension
François Bernard, Enrique Chávez-Martínez, Arturo E. Giles Flores
We describe the semigroup of the Lipschitz saturation of a complex analytic toric singularity in arbitrary dimension. We give a necessary and sufficient condition for a monomial in…
Formal splitting and stack-theoretic normal crossings desingularization
André Belotto da Silva, François Bernard, Edward Bierstone
We show that stack-theoretic resolution of singularities preserving normal crossings (partial desingularization) by weighted blowings-up, can be obtained in a simple direct way fro…
Seminormal toric varieties
François Bernard, Antoine Boivin
In this paper, we provide a combinatorial description of seminormal toric varieties. The corresponding combinatorial object is a fan equipped with a collection of groups assigned t…
Seminormalization and regulous functions on complex affine varieties
François Bernard
We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidea…