代数幾何学セミナー

開催情報	金曜日　13:30～15:00　数理科学研究科棟(駒場) 118号室
担当者	權業善範、河上龍郎、榎園誠

2017年05月16日(火)

15:30-17:00 数理科学研究科棟(駒場) 122号室
古川勝久氏 (東大数理)
On separable higher Gauss maps (English)

[ 講演概要 ]
We study the

$m$ -th Gauss map in the sense of F. L. Zak of a projective variety

$X ¥subset P^N$ over an algebraically closed field in any characteristic, where

$m$ is an integer with

$n:= ¥dim(X) ¥leq m < N$ . It is known that the contact locus on

$X$ of a general tangent

$m$ -plane can be non-linear in positive characteristic, if the

$m$ -th Gauss map is inseparable.

In this talk, I will explain that for any

$m$ , the locus is a linear variety if the

$m$ -th Gauss map is separable. I will also explain that for smooth

$X$ with

$n < N-2$ , the

$(n+1)$ -th Gauss
map is birational if it is separable, unless

$X$ is the Segre embedding

$P^1 ¥times P^n ¥subset P^{2n-1}$ . This is related to L. Ein's classification of varieties with small dual varieties in characteristic zero.

This talk is based on a joint work with Atsushi Ito.

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