Keywords

• F-singularity
• geometric vertex decomposition
• Frobenius splittings

Abstract In this talk we explore $F$-purity of geometrically vertex decomposable ideals. After a brief overview of some basic concepts in $F$-singularity theory and geometric vertex decomposition, we present a way to iteratively construct Frobenius splittings for certain geometric vertex decomposable ideals. This technique will be illustrated with examples.