Algebraic geometry, which roughly speaking studies geometric objects defined by polynomials (called varieties), is one of the largest fields in mathematics today and has wide applications both in technology and physics.
Classifying varieties is one of the most important topics in the field and has undergone a major development in the past 20 years. Despite the fact that many new results have been proved, many questions still remain open. The aim of the project is to develop further, generalize and find more applications of a new method recently developed by the researcher and the scientist in charge at the host institution and already applied successfully to certain three-dimensional varieties.
The method is based upon reducing classification questions to the study of certain maps on curves in the varieties and works particularly well when the varieties have "many'' subvarieties. The project especially aims at finding results for important varieties arising in modern classification theory, such as Mori fiber spaces and Calabi-Yau varieties. The latter constitute a big gap in today's knowledge, because the existing methods are insufficient.
At the same time Calabi-Yau varieties play a very important role in modern theoretical physics, so any result on their classification will be of big interest also outside of algebraic geometry. The project will make the researcher increase his research skills on higher dimensional varieties and allow him to collaborate with many experts, both in the area of the project and in many areas complementary to it.
As he will coordinate the collaborations and regularly present the latest results in seminars, he will improve both his leading and presentation skills. A further aim is to build the basis for a long time interaction between Norway and Italy in algebraic geometry.
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