October 25,  2024

on-line on zoom

• 15:30-16:20 Grzegorz Oleksik (Politechnika Poznańska) On the generic dimension of analytic sets

  Abstract: Let \(f\) be a germ of the Mondal non-degenerate map, which defines a germ of an analytic set \(X = V(f)\). In this article we give a combinatorial characterization of the local dimension of \(X\) in terms of supports \(f_i.\) We also show that this dimension can be read off from the Newton polyhedrons of \(f_i.\) As a corollary we show how to read off the dimension of the critical locus of singularity from its Newton diagram.

• 16:30 - 17:20 Michał Farnik (Uniwersytet Jagielloński) Generic symmetry defect set of plane algebraic curves
  

  Abstract:  Let \(X^r, Y^s \subset \mathbb{C}^{n}\) be (not necessarily distinct) smooth algebraic varieties in general position of dimensions \(r\) and \(s\), where \(r+s=n\). The symmetry defect set of \(X\) and \(Y\) is the bifurcation set of the midpoint map \(\Phi: X\times Y \ni (x,y)\mapsto (x+y)/2 \in \mathbb{C}^{n}\). It is a hypersurface but in general it has bad singularities.
  I will introduce the algebraic version of the generic symmetry defect set of \(X\) and \(Y\) which has only Thom-Boardman singularities. Then I will compute its singularities for \(X\) and \(Y\) being smooth plane curves transversal to the line at infinity. This is joint work with L.R.G. Dias and Z. Jelonek.