Research

My domains of research are singularity theory and algebraic geometry.

Preprints :

• Lipschitz saturation of toric singularities in any dimension.
  F. Bernard, E. Chávez-Martínez, A.E. Giles Flores, 2026 [arXiv]

• Formal splitting and stack-theoretic normal crossings desingularisation.
  A. Belotto da Silva, F. Bernard, E. Bierstone, 2026 [arXiv]

Publications :

• Seminormal toric varieties.
  F. Bernard, A. Boivin, 2026 [arXiv], To appear in Journal of Pure and Applied Algebra

• Relative Lipschitz saturation of complex algebraic varieties.
  F. Bernard, 2025 [arXiv][AG], Advances in Geometry.

• A notion of seminormalization for real algebraic varieties.
  F. Bernard, 2024 [arXiv][JLMS], Journal of the London Mathematical Society.

• Algebraic characterizations of homeomorphisms between algebraic varieties.
  F. Bernard, G. Fichou, J.-P. Monnier, R. Quarez, 2024 [arXiv][MZ], Mathematische Zeitschrift.

• Seminormalization and regulous functions on complex algebraic varieties.
  F. Bernard, 2025 [arXiv][AIF], Annales de l'Institut Fourier.