# Featured Paper of the Week

## Akizuki-Nakano vanishing theorem and its application for globally F-split 3-folds

2020-01-09

In algebraic geometry, it is important to study spaces (=varieties) which may admit singular points. "Smoothing" is an effective way to deal with singularities. Roughly speaking, a smoothing of a (singular) variety helps us to find another variety which is non-singular and is "similar" to the original variety. Namikawa proved that a complex Fano 3-fold whose singular points are at worst ordinary double points admits a smoothing. In this paper, we give an analogy of this result in the case where the Fano variety is not complex, but is defined over a field of positive characteristic. The key ingredient of the proof is the vanishing of the second cohomology of the tangent space, which is a vector space containing an obstruction to construct a smoothing. We prove a positive characteristic analogue of the Akizuki-Nakano type vanishing for 3-dimensional varieties and as a corollary, we conclude the result about a smoothing.

Reference:
Kenta Sato, Shunsuke Takagi
"Weak Akizuki-Nakano vanishing theorem for globally $F$-split 3-folds"
arXiv: 1912.12074

# Upcoming Events

## Seminar

### Tipping point detection of nonlinear dynamics by dynamic network biomarkers, and short-term time-series data prediction by randomly distributed embedding

January 15 at 14:00 - 16:30, 2020

Dr. Luonan Chen (Professor, Excutive director, Chinese Academy of Sciences, China)

He will talk about theoretical study on complex network data, including clinical data.

His talk consists of two parts:
14:00-15:00: Detecting the tipping points of dynamic processes by dynamic network biomarkers
15:00-15:30: Coffee break
15:30-16:30: Predicting future dynamics of short-term time-series data by randomly distributed embedding

First part of his talk is for general audience.
In second part of his talk, he will explain mathematical basis of his study in detail.

Event Official Language: English

## Colloquium

iTHEMS Colloquium

### Exploring the learning principle in the brain

January 16 at 15:30 - 17:00, 2020

Dr. Taro Toyoizumi (Team Leader, RIKEN Center for Brain Science (CBS))

Broadcast: R311, Computational Science Research Building, R-CCS, Kobe Campus, RIKEN / SUURI-COOL (Kyoto), #204-205, 2F Maskawa Building for Education and Research, North Campus, Kyoto University / SUURI-COOL (Sendai), #303, 3F AIMR Main Building, Advanced Institute for Materials Research (AIMR), Tohoku University

Event Official Language: English

## Seminar

iTHEMS Math Seminar

### Semiclassical methods in mathematical quantum mechanics

January 23 at 16:00 - 18:10, 2020

Dr. Shu Nakamura (Professor, Gakushuin University)

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Event Official Language: English

## Workshop

### Workshop on quantum information science

January 29 at 10:00 - 18:00, 2020

Event Official Language: Japanese

# Upcoming Visitors

January 22 - 24, 2020

### Dr. Hiroyuki Fuji

Kagawa University

Visiting Place: Main Research Building

January 22 - 24, 2020

### Mr. Koyanagi Yuki

Student Trainee, iTHEMS / Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark

Research fields: Mathematical Biology

Visiting Place: Main Research Building