250093 VO Singularitäten algebraischer Varietäten (2020W)

Singularities of algebraic or analytic varieties are points where the variety is not smooth, i.e., not locally diffeomorphic to a linear space. Examples of surface with singularities can be seen on

https://homepage.univie.ac.at/herwig.hauser/gallery.html

The study of these singular points is important for understanding the geometry and properties of varieties, both real and complex and, on the arithmetic side, over finite fields. It combines techniques from algebra, analysis and differential geometry. We will discuss tangent spaces, deformations, symmetry groups, hyperplane sections and the resolution of singularities by normalization and blowups. The course shall prepare to write Master's theses on related topics.