Welcome to KAJI's Home Page
japanese page
Hajime KAJI, Professor
Department of Mathematics
School of Science and Engineering
Waseda University
address: Shinjuku, Tokyo 169-8555, JAPAN
office: Room 51-18-07B, Nishi-Waseda Campus
phone: +81-3-5286-3347
fax: +81-3-5286-3483
e-address: kaji[at]waseda.jp

Research Interests

I am interested in projective geometry of algebraic varieties: recently I am making researches on Gauss maps of projective varieties in positive characteristic as well as on secant varieties of projective varieties, especially, homogeneous projective varieties (that is, projective varieties on which some complex algebraic groups act transitively).

Keywords: projective variety, Gauss map, conormal variety, projective dual, secant variety, graded Lie algebra, triple system, ...

Recent Works
  1. Higher Gauss Maps of Veronese Varieties---a generalization of Boole's formula---, Comm. Algebra 46 (2018), no. 9, 4064--4078. [arXiv:1509.04935].
  2. Degree Formulae for Grassmann Bundles, II (with T. Terasoma), preprint [arXiv:1508.01663].
  3. Degree formula for Grassmann bundles (with T. Terasoma), Journal of Pure and Applied Algebra 219 (2015), 5426-5428.
  4. On the tangentially degenerate curves, II, "the Kleiman-Simis volume," the Bulletin of the Brazilian Mathematical Society 45 (2014), 748-752.
  5. Projective varieties admitting an embedding with Gauss map of rank zero (with S. Fukasawa, K. Furukawa), Advances in Mathematics 224 (2010), 2645-2661 [online].
  6. Any algebraic variety in positive characteristic admits a projective model with inseparable Gauss map (with S. Fukasawa), J. Pure and Applied Algebra 214 (2010), 297--300 [online].
  7. The separability of the Gauss map versus the reflexivity, "the Proceedings of the IV Iberoamerican Conference on Complex Geometry (Ouro Preto, Minas Gerais, Brasil, August 12--18, 2007)," Geometriae Dedicata 139 (2009), 75--82 [online].
  8. The reflexivity of a Segre product of projective varieties (with S. Fukasawa), Math. Annalen 342 (2008), 279--289 [on line].
  9. Existence of a non-reflexive embedding with birational Gauss map for a projective variety (with S. Fukasawa), Math. Nachrichten 281 (2008), 1412--1417.
  10. The separability of the Gauss map and the reflexivity for a projective surface (with S. Fukasawa), Math. Zeitschrift 256 (2007), 699--703.
  11. The classification of orbits by a natural action of certain reductive linear grouup (with O. Yasukura), Yokohama Math. J. 53 (2006), 39--61.
A complete list is here. If you have any trouble in getting the files above, please let me know.

Brief Vita
B.Sc., Waseda University, 1982
M.Sc., Waseda University, 1984
D.Sc., Waseda University, 1987 (supervisor: Prof. Satoshi ARIMA)
Research Associate, Waseda University, 1987-1989
Research Associate, Yokohama City University, 1989-1993
Associate Professor, Waseda University, 1993-1999
Professor, Waseda University, 1999-

gateway to the Ka-dimensional space
Ka-dimensional space/豕莱桾瘠

I am nerdier than 94% of all people. Are you a nerd? Click here to take the Nerd Test, get nerdy images and jokes, and talk on the nerd forum!