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Algebraic Geometry Seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
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)
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).
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).
