イベントカレンダー
- 日程
- 2022年10月21日（金）
- 時間
- 16:30～18:00
- 場所
- 本館２階Ｈ２２４セミナー室で対面、Zoomのハイブリッド形式で開催する予定です。（会場が変更になりました）
Zoom URLは講演開始までに http://www.math.titech.ac.jp/~honda/index.html にてお知らせします。
- 講師
- 服部 真史 氏（京都大理学部）
詳細は http://www.math.titech.ac.jp/~honda/index.html を参照してください。
- 講演タイトル
- On K-stabilty of algebraic fiber spaces
- アブストラクト
-
In K-stability, the characterization of K-stable varieties is well-studied when $K_X$ is ample or $X$ is a Calabi-Yau or Fano variety. The cscK problem of smooth fibrations was also studied by Fine and Dervan-Sektnan. Nevertheless, K-stability of a fibration with a singular fiber is not known much. We introduce adiabatic K-stability (If $f:(X,H)\to (B,L)$ is a fibration of polarized varieties, this means that K-stability of $(X,aH+L)$ for sufficiently small $a$) and show that adiabatic K-semistability of Calabi-Yau fibration (i.e., $K_X$ is relatively trivial) implies log-twisted K-semistability of the base variety by applying the canonical bundle formula. If the base is a curve, we also obtain a partial converse. In this talk, I would like to explain a sufficient condition for the existence of cscK metrics on rational elliptic surfaces as an application of our main result. In addition, I would like to explain our result on K-stability of relatively K-ample fibered surfaces.
更新日：2022.08.25
