Research Institute for Mathematical Sciences

Research

Shigeru Mukai is working on the moduli theory of algebraic varieties and vector bundles, and applying it to the study of algebraic varieties such as K3 surfaces, Enriques surfaces and Fano varieties. For example he classified 3-dimensional Fano varieties using vector bundles of higher rank and their deformation. In connection with moduli construction, he is interested in invariant theory. He poses the problem "Are the invariant rings finitely generated when the 2-dimensional additive group acts linearly on polynomial rings?" in his study of Nagata's counter-example of Hilbert's fourteenth problem. Recently he is working on Enriques surfaces using Torelli type theorem and root systems governing the arrangements of smooth rational curves on them.