Understanding when stable vector bundles with fixed topological invariants exist---or fail to exist---is a longstanding and difficult problem. While there are many topological obstructions, algebraic ones are rarer: beyond the classical Bogomolov inequality, which gives a quadratic bound in terms of the rank and the first two Chern characters, few general tools are available. In higher dimensions, one expects…

Del Pezzo surfaces and their automorphism groups play a key role in the classification up to conjugacy of finite subgroups of the Cremona group of the plane. Over an algebraically closed field, they are completely classified together with their automorphism groups. In this talk, we will focus on real rational Del Pezzo surfaces of degree 4. Unlike larger degrees, the…