Algebraic Geometry Seminar

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Date, time & place Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu

2011/05/02

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Katsuhisa Furukawa (Waseda University)
Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)
[ Abstract ]
I will talk about the study of Gauss map in positivity characteristic which is a joint work with S. Fukasawa and H. Kaji. I will also talk about my resent research of this topic.

We call that a projective variety $X$ satisfies (GMRZ) if there exists an embedding $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ whose Gauss map $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ is of rank zero at a general point.

We study the case where $X$ has a rational curve $C$. Then, as a fundamental theorem, it follows that the property (GMRZ) makes the splitting type of the normal bundle $N_{C/X}$ very special. We also have a characterization of the Fermat cubic hypersurface in characteristic two in terms of (GMRZ). In this talk, I will also explain the relation of blow-ups and the property (GMRZ).