You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar.
Speaker: Öznur Turhan (Galatasaray & Polish Academy)
“Newton-nondegenerate line singularities, Lê numbers and Bekka (c)-regularity”
Abstract: Consider an analytic function f(t,z) defined in a neighbourhood of the origin of C x Cn such that for all t, the function ft(z):=f(t,z) defines a hypersurface of Cn with a line singularity at 0∈Cn . Denote by V(f) the hypersurface of C x Cn defined by f(t,z) and write Σf for its singular locus. We assume that ft is ”quasi-convenient” and Newton nondegenerate. Within this framework, we show that if the Lê numbers of ft are independent of t for all small t, then Σf is smooth and V(f)\Σf is Bekka (c)-regular over Σf. This is a version for line singularities of a result of Abderrahmane concerning isolated singularities.
As a corollary, we obtain that any family of quasi-convenient, Newton non-degenerate, line singularities with constant Lê numbers as above is topologically equisingular. In particular, this applies to families with non-constant Newton diagrams, and therefore extends, in some direction, a result previously observed by Damon.
This is a joint work with Christophe Eyral.
Date: 20 February 2026, Friday
Time: 15:40 (GMT+3)
Place: Zoom
This is an online seminar. To request the Zoom link, please send a message to sertoz@bilkent.edu.tr