Seminár z algebraickej geometrie - Peter Schenzel (7.9.2022)

v stredu 7.9.2022 o 10:00 hod. v miestnosti M/116

31. 08. 2022 20.49 hod.
Od: Pavel Chalmoviansky

Prednášajúci: prof. Peter Schenzel (Univerzita Martina Luthera, Halle-Wittenberg)

Názov: On Families of Point Blowups of the Real Affine Plane

Termín: 7.9.2022, 10:00 hod., miestnosť M/116


We study the blow-up of a finite number of points $X$ in the real affine plane, where $X$ is defined by the vanishing of two polynomials $f$ ang $g$. The blow-up is a helpful tool for the desingularization also in higher dimensions. The subject is illustrated by the desingularization of the singular cubic and the lemniscate. For the visualization we introduce the concept of toroidal embedding of the blow-up, illustrated by the construction of the Möbius strip and the Whitney umbrella. The visualization of the toroidal blow-up is done by the system RealSurf. The main subject of the talk will be the study of certain deformations of the defining equations by $f_d$ and $g_d$ of the point set $X$. We will discuss the classification problem and the deformation problem for families of different blow-ups of $X$. There are some problems and comments and in particular the visualization of some examples of deformations.