代数幾何学セミナー

過去の記録 ~05/01次回の予定今後の予定 05/02~

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 

2024年10月04日(金)

13:30-15:00   数理科学研究科棟(駒場) 118号室
高松哲平 氏 (京都大学)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
[ 講演概要 ]
Fano threefolds over C with Picard number and index equal to 1 are known to be classified by their genus g (where 2≤g≤12 and g≠11). In particular, Mukai has shown that those with genus 7 can be described as hyperplane sections of a connected component of the 10-dimensional orthogonal Grassmannian.
In this talk, we discuss the arithmetic properties of these genus 7 threefolds and their higher-dimensional generalizations (called Mukai varieties of genus 7). More precisely, we consider the finiteness problem of varieties over a ring of S-integers (so called the Shafarevich conjecture), and the existence problem of varieties over the rational integer ring Z.
This talk is based on a joint work with Tetsushi Ito, Akihiro Kanemitsu, and Yuuji Tanaka.