You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar.<\/p>\n
Speaker: \u00d6znur Turhan (Galatasaray & Polish Academy)<\/p>\n
\u201cNewton-nondegenerate line singularities, L\u00ea numbers and Bekka (c)-regularity\u201d<\/p>\n
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\u2208Cn . Denote by V(f) the hypersurface of C x Cn defined by f(t,z) and write \u03a3f for its singular locus. We assume that ft is \u201dquasi-convenient\u201d and Newton nondegenerate. Within this framework, we show that if the L\u00ea numbers of ft are independent of t for all small t, then \u03a3f is smooth and V(f)\\\u03a3f is Bekka (c)-regular over \u03a3f. This is a version for line singularities of a result of Abderrahmane concerning isolated singularities.<\/p>\n
As a corollary, we obtain that any family of quasi-convenient, Newton non-degenerate, line singularities with constant L\u00ea 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.<\/p>\n
This is a joint work with Christophe Eyral.<\/p>\n
Date: 20 February 2026, Friday
\nTime: 15:40 (GMT+3)
\nPlace: Zoom<\/p>\n
This is an online seminar. To request the Zoom link, please send a message to sertoz@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar. Speaker: \u00d6znur Turhan (Galatasaray & Polish Academy) \u201cNewton-nondegenerate line singularities, L\u00ea numbers and Bekka (c)-regularity\u201d 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) [\u2026] <\/p>\n