Seminar on Geometric Complex Analysis

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama

2023/11/27

11:00-12:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Ogawa (Osaka Metropolitan University)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
[ Abstract ]
Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A