Updated on 2023/04/26

写真a

 
EJIRI SHO
 
Organization
Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics
Title
Associate Professor
Affiliation
Institute of Science

Position

  • Graduate School of Science Department of Mathematics 

    Associate Professor  2023.04 - Now

  • School of Science Department of Mathematics 

    Associate Professor  2023.04 - Now

Degree

  • 博士（数理科学） （ The University of Tokyo ）

  • 修士（数理科学） （ The University of Tokyo ）

  • 学士（理学） （ Kobe University ）

Research Areas

  • Natural Science / Algebra  / Algebraic geometry

Research Interests

  • Iitaka's conjecture

  • Algebraic geometry in positive characteristic

  • Positivity theorems

  • Algebraic fiber spaces

  • Albanese morphisms

  • Abelian varieties

Job Career (off-campus)

  • Osaka Metropolitan University   Department of Mathematics

    2023.04 - Now

  • Osaka Metropolitan University   Osaka Central Advanced Mathematical Institute   Post Doctor

    2022.04 - 2023.03

  • Swiss Federal Institute of Technology in Lausanne   School of Basic Sciences, Institute of Mathematics   Post Doctor

    2021.08 - 2021.10

  • Osaka University   Graduate School of Science Department of Mathematics   Post doctor

    2018.04 - 2021.07

Papers

  • Direct images of pluricanonical bundles and Frobenius stable canonical rings of fibers

    Sho Ejiri

    to appear in Algebraic Geometry   2023.03

  • On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces Reviewed

    Sho Ejiri, Masataka Iwai, Shin-ichi Matsumura

    Journal of Algebraic Geometry   2023.01（ ISSN:1056-3911 ） （ eISSN:1534-7486 ）

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    Publishing type：Research paper (scientific journal)  

    <p>In this paper, we study the relative anti-canonical divisor of an algebraic fiber space , and we reveal relations among positivity conditions of , certain flatness of direct image sheaves, and variants of the base loci including the stable (augmented, restricted) base loci and upper level sets of Lelong numbers. This paper contains three main results: The first result says that all the above base loci are located in the horizontal direction unless they are empty. The second result is an algebraic proof for Campana–Cao–Matsumura’s equality on Hacon–M<sup>c</sup>Kernan’s question, whose original proof depends on analytics methods. The third result proves that algebraic fiber spaces with semi-ample relative anti-canonical divisor actually have a product structure via the base change by an appropriate finite étale cover of . Our proof is based on algebraic as well as analytic methods for positivity of direct image sheaves.</p>

    DOI： 10.1090/jag/814

  • On the abundance theorem for numerically trivial canonical divisors in positive characteristic

    Ejiri S.

    Journal fur die Reine und Angewandte Mathematik   2022 ( 789 )   253 - 264   2022.08（ ISSN:00754102 ）

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  • Subadditivity of Kodaira dimension does not hold in positive characteristic Reviewed

    Paolo Cascini, Sho Ejiri, János Kollár, Lei Zhang

    Commentarii Mathematici Helvetici   96 ( 3 )   465 - 481   2021.11（ ISSN:0010-2571 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.4171/cmh/517

  • Positivity of anticanonical divisors and F-purityof fibers Reviewed

    Sho Ejiri

    Algebra & Number Theory   13 ( 9 )   2057 - 2080   2019.12（ ISSN:1937-0652 ） （ eISSN:1944-7833 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.2140/ant.2019.13.2057

  • A Characterization of Ordinary Abelian Varieties by the Frobenius Push-Forward of the Structure Sheaf II Reviewed

    Sho Ejiri, Akiyoshi Sannai

    International Mathematics Research Notices   2019 ( 19 )   5975 - 5988   2019.10（ ISSN:1073-7928 ） （ eISSN:1687-0247 ）

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    Publishing type：Research paper (scientific journal)  

    <title>Abstract</title>
    In this paper, we prove that a smooth projective variety X of characteristic p &gt; 0 is an ordinary abelian variety if and only if KX is pseudo-effective and $F_{*}^{e}{\mathcal {O } }_{X}$ splits into a direct sum of line bundles for an integer e with pe &gt; 2.

    DOI： 10.1093/imrn/rnx288

  • When is the Albanese morphism an algebraic fiber space in positive characteristic? Reviewed

    Sho Ejiri

    manuscripta mathematica   160 ( 1-2 )   239 - 264   2019.09（ ISSN:0025-2611 ） （ eISSN:1432-1785 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00229-018-1056-6

    Other URL： http://link.springer.com/article/10.1007/s00229-018-1056-6/fulltext.html

  • Nef anti-canonical divisors and rationally connected fibrations Reviewed

    Sho Ejiri, Yoshinori Gongyo

    Compositio Mathematica   155 ( 7 )   1444 - 1456   2019.07（ ISSN:0010-437X ） （ eISSN:1570-5846 ）

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    Publishing type：Research paper (scientific journal)  

    We study the Iitaka–Kodaira dimension of nef relative anti-canonical divisors. As a consequence, we prove that given a complex projective variety with klt singularities, if the anti-canonical divisor is nef, then the dimension of a general fibre of the maximal rationally connected fibration is at least the Iitaka–Kodaira dimension of the anti-canonical divisor.

    DOI： 10.1112/s0010437x19007383

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MISC

  • Varieties in positive characteristic with numerically flat log cotangent bundle

    Sho Ejiri, Shou Yoshikawa

    2023.03

  • Numerical Kodaira dimension of algebraic fiber spaces in positive characteristic

    Sho Ejiri

    2022.12

  • Notes on direct images of pluricanonical bundles

    Sho Ejiri

    2022.10

  • Notes on Frobenius stable direct images

    Sho Ejiri

    2022.10

Presentations

  • Subadditivity of Kodaira dimension does not hold in positive characteristic Invited

    Sho Ejiri

    2021.10 

    　More details

    Presentation type：Oral presentation (invited, special)  

  • On the abundance theorem for numerically trivial canonical divisors in positive characteristic Invited

    Sho Ejiri

    Princeton Algebraic Geometry Seminar  2021.03 

  • Subadditivity of Kodaira dimension does not hold in positive characteristic Invited

    Sho Ejiri

    2020.11 

  • On positivity of relative anti-canonical divisors Invited

    Sho Ejiri

    2020.04 

  • Nef anti-canonical divisors and rationally connected fibrations Invited

    Sho Ejiri

    Algebraic Geometry Seminar  2020.03 

  • Iitaka's conjecture in positive characteristic and related topics Invited

    Sho Ejiri

    2020.01 

  • On relative versions of Fujita’s freeness conjecture in positive characteristic Invited

    Sho Ejiri

    Tokyo–Seoul Conference in Mathematics 2019  2019.11 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    2019.11 

  • On extensions of Iitaka’s conjecture to positive characteristic Invited

    Sho Ejiri

    Groups, Arithmetic and Algebraic Geometry Seminar  2019.10 

  • Iitaka's conjecture and weak positivity theorem in positive characteristic Invited

    Sho Ejiri

    Young mathematicians workshop on algebraic, geometric, and analytic aspects of K-theory and vector bundles  2019.08 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    Workshop on Algebraic Geometry  2019.07 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    2019.07 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    Seminar of algebraic geometry  2019.06 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    Algebra & Combinatorics Seminar  2019.06 

  • On direct images of pluricanonical bundles in positive characteristic Invited

    Sho Ejiri

    2019.04 

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Grant-in-Aid for Scientific Research

  • 正標数の代数的ファイバー空間の研究

    Grant-in-Aid for Early-Career Scientists  2028

  • 正標数の代数的ファイバー空間の研究

    Grant-in-Aid for Early-Career Scientists  2027

  • 正標数の代数的ファイバー空間の研究

    Grant-in-Aid for Early-Career Scientists  2026

  • 正標数の代数的ファイバー空間の研究

    Grant-in-Aid for Early-Career Scientists  2025

  • 正標数の代数的ファイバー空間の研究

    Grant-in-Aid for Early-Career Scientists  2024

Charge of on-campus class subject

  • 数学基礎演習1

    2024   Weekly class   Undergraduate

  • 数学特別研究1A

    2024   Intensive lecture   Graduate school

  • 代数学特論B

    2024   Weekly class   Graduate school

  • 数学特別研究2A

    2024   Intensive lecture   Graduate school

  • 数学特別研究5A

    2024   Intensive lecture   Graduate school

  • 数学特別研究4A

    2024   Intensive lecture   Graduate school

  • 数学特別研究3A

    2024   Intensive lecture   Graduate school

  • 代数学講義Ⅱ

    2024   Weekly class   Undergraduate

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