Title: Weighted Projective Spaces and Complete Intersections
Speaker: Alessandro Passantino
Abstract: Weighted Projective Spaces are projective varieties which generalise classical projective spaces; they give new tools to construct explicit families of varieties whose properties can be determined by properly choosing some parameters. For this reason, they are ubiquitous in birational geometry as they allow for a framework in which particular cases of conjectures can be studied, or explicit results can be obtained through sheer computation. In this talk, we will first introduce weighted projective spaces, weighted complete intersections (WCI for short) and their properties, then we will give some examples of how WCIs are used in recent results regarding open problems in birational geometry. We will conclude with an example of how deep the connection between geometrical and numerical properties can go, by showing how a conjecture in birational geometry and a problem in classical number theory are tightly related.
Some snacks will be provided before and after the talk.