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# 【ハイブリッド開催】東工大 幾何セミナー：服部 真史 氏

2022年10月21日（金）

16:30～18:00

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。

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.

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