My field of expertise is algebraic geometry. There we consider a set of zero points (algebraic variety) of polynomials. For example, lines, circles, hyperbolas, and parabolas are algebraic varieties. The set of all geometric objects with certain properties is called a moduli space.
Moduli spaces of stable vector bundles on complex algebraic surfaces X are actively investigated as concrete examples of algebraic varieties.

For an algebraic variety M, the Kodaira dimension is determined.
The Kodaira dimension of M is an important invariant related to the curvature of M. Also, there is the minimal model theory to understand higher dimensional varieties. In this theory, one simplifies a variety by exploding and contracting its subspaces to get a simple variety, called minimal model.

I am interested in singularities, the Kodaira dimenson and the minimal model program of moduli space M.
(1) For large classes of surfaces X, I described the minimal model program of M by using words of moduli theory.
(2) I examined singularities of M, and in case where the structure of X is relatively simple, I showed that singularities of M are “good”. As a result, I calculated the Kodaira dimension of M.