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Séminaire de Géométrie

Partial desingularization preserving normal crossings

André Belotto

( (IMJ Paris) )

Salle 2

le 15 novembre 2024 à 10:45

Can we understand the nature of the singularities that have to be admitted after a blow-up sequence that preserves the normal crossings locus of an algebraic (or complex-analytic) variety X? For example, every surface can be transformed by blowings-up preserving normal crossings to a surface with at most additional Whitney umbrella singularities. We will discuss general conjectures in arbitrary dimensions, and partial solutions. The techniques involve circulant matrices, elementary Galois theory and Newton-Puiseux expansion in several variables. We will discuss results in collaboration with Edward Bierstone and Ramon Ronzon Lavie.