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Algebraic Geometry Seminar
Seminar information archive ～10/06｜Next seminar｜Future seminars 10/07～
| 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 |
2024/10/04
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Teppei Takamatsu (Kyoto University)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
Teppei Takamatsu (Kyoto University)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
[ Abstract ]
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.
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.
