# Faculty

## Kayo Masuda

### Major research activity

A complex algebraic variety is the set of roots of a finite number of polynomial equations with coefficients in the complex number field C. An algebraic variety of dimension one is called an algebraic curve and that of dimension two an algebraic surface.

The simplest example of an algebraic curve is the affine line C and that of an algebraic surface is the affine plane C^{2}. The structure of algebraic varieties of dimension less than three is fairly well-understood. However, the structure of algebraic varieties of higher dimension is far from well-known at the present.

In our laboratory, we study the structure of algebraic varieties especially from the viewpoint of algebraic group actions. For example, suppose that a smooth contractible (affine) algebraic surface is given. Can we say it is isomorphic to the affine plane C^{2}? If we have information about symmetries, namely, the group actions on the algebraic surface, we can determine whether the surface is isomorphic to the plane or not.

### Major relevant publications

- K. Masuda, Characterizations of hypersurfaces of a Danielewski type, Journal of Pure and Applied Algebra 218 (2014) 624-633.
- K. Masuda, Equivariant derivations and the additive group actions, Affine Algebraic Geometry, CRM Proceedings and Lecture Notes 54 (2011), 231-242
- K. Masuda, Homogeneous locally nilpotent derivations having slices and embeddings of affine spaces, J. Algebra 321 (2009), 1719-1733
- Gurjar, R. V.; Masuda, K.; Miyanishi, M. A1-fibrations on affine threefolds. J. Pure Appl. Algebra 216 (2012), no.2, 296-313.
- Gurjar, Rajendra V.; Masuda, Kayo; Miyanishi, Masayoshi Deformations of A1-fibrations. Automorphisms in birational and affine geometry, 327-361, Springer Proc. Math. Stat., 79, Springer, Cham, 2014.