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iTHEMS Weekly News Letter

Featured Paper of the Week

Dr. Kenta Sato thumbnail

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

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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:
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Semiclassical methods in mathematical quantum mechanics

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

Dr. Shu Nakamura (Professor, Gakushuin University)

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Venue: #435-437, Main Research Building, RIKEN

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January 22 - 24, 2020

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Kagawa University

Visiting Place: Main Research Building

Mr. Koyanagi Yuki thumbnail

January 22 - 24, 2020

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Student Trainee, iTHEMS

Research fields: Mathematical Biology

Visiting Place: Main Research Building

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