## Staff -MUKAI, Shigeru-

Name

**MUKAI, Shigeru**
Position
Professor

E-Mail
mukai (email address: add @kurims.kyoto-u.ac.jp)

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 following problem in his
study of Nagata's counter-example of Hilbert's fourteenth problem. "Are
the invariant rings finitely generated when the 2-dimensional additive
group acts linearly on polynomial rings?" Recently he is working on
Enriques surfaces using their root systems governing the arrangements of
smooth rational curves on them. Jointly with H. Ohashi, he recently
generalized the relation between the Mathieu groups and finite
symplectic automorphisms of K3 surfaces to Enriques surfaces.