# Katsuhisa FURUKAWA

(Last modified date: 12 May 2014)

## Research interest

My research subject is *Algebraic Geometry*.
In particular, I am interested in the following topics:

- Projective geometry in arbitrary characteristic
(Gauss maps of projective varieties, projective duality, etc).
- Characterization of basic projective varieties (projective space, hyperquadric, Fermat hypersurface in positive characteristic, etc).
- Theory of rational curves on algebraic varieties.

## Works

### Papers

*Cohomological characterization of hyperquadrics of odd dimensions in characteristic two*,
to appear in Mathematische Zeitschrift, DOI: 10.1007/s00209-014-1308-4.

[online]
[arXiv]

*Duality with expanding maps and shrinking maps, and its applications to Gauss maps*,
Mathematische Annalen **358**
(2014)
403—432.

[online]
[arXiv]

*Cubic hypersurfaces admitting an embedding with Gauss map of rank 0*,
Advances in Mathematics **230**
(2012)
1174—1183.

[online]

*Rational curves on hypersurfaces*,
Journal für die reine und angewandte Mathematik (Crelles Journal) **665**
(2012)
157—188.

[online]

*Defining ideal of the Segre locus in arbitrary characteristic*,
Journal of Algebra **336**
(2011)
84—98.

[online]

*Projective varieties admitting an embedding with Gauss map of rank zero*
(with S. Fukasawa and H. Kaji),
Advances in Mathematics **224**
(2010)
2645—2661.

[online]

### Preprints

*Gauss maps of toric varieties*
(with A. Ito),
arXiv:1403.0793v1, 25pages.

[arXiv]

*Convex rationally connected varieties in arbitrary characteristic*,
arXiv:1311.6181v1, 15pages.

[arXiv]

*On general fibers of Gauss maps in arbitrary characteristic*,
arXiv:1310.5387v2, 21pages.

[arXiv]

### Seminar

I am an organizer of *Waseda Algebraic Geometry Seminar*
[webpage].

## Addresses

Department of Mathematics, School of Fundamental Science and Engineering, Waseda University,

Ohkubo 3-4-1, Shinjuku, Tokyo, 169-8555, Japan

E-mail: katu at aoni.waseda.jp