since 2000

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This week the ODTÜ-Bilkent Algebraic Geometry Seminar  is online

This talk will begin at 15:40 (GMT+3)
Please check your time difference between Ankara and your city here
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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.

You are most cordially invited to attend.

Ali Sinan Sertöz

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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail: sertoz@bilkent.edu.tr 
Web: sertoz.bilkent.edu.tr 
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