Table Of ContentProceedings of the Conference
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Proceedings of the Conference
Osaka, Japan 3 – 6 March 2011
Editors
Kayo Masuda
Kwansei Gakuin University, Japan
Hideo Kojima
Niigata University, Japan
Takashi Kishimoto
Saitama University, Japan
World Scientific
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AFFINE ALGEBRAIC GEOMETRY
Proceedings of the Conference
Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd.
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DEDICATION
Professor Masayoshi Miyanishi was born in 1940. He entered Kyoto
University in 1958 and started his career as a mathematician in the very
stimulating atmosphere. Around 1960, there was a very strong school of
algebraic geometry in Kyoto. Professor Nagata was one of the leaders of
this school. Under the leadership of Professor Nagata, several brilliant
students of Professor Miyanishi’s generation worked hard to absorb new
languageandtheoriesinalgebraicgeometry.Infact,the firstbook ofEGA
waspublishedin1960andatthattime the greatrevolutionwasperformed
in algebraic geometry. To those young mathematicians who studied with
Professor Miyanishi belonged Professors T. Oda, T. Miyata, H. Sumihiro
and M. Maruyama. They later became leaders of algebraic geometry in
Japan.
After finishinghismasterthesis,ProfessorMiyanishibecamearesearch
assistantandthenaninstructorofKyotoUniversity.Hereceivedhis Ph.D.
in1968fromKyotoUniversity.Afterwardshebecameanassociateprofessor
at OsakaUniversity in 1973and a professorin 1984which he kept until he
retired from Osaka University in 2003. He was a professor of mathematics
in Kwansei Gakuin University from 2003 to 2009.
Professor Miyanishi visited several foreign countries and had opportu-
nities to do fruitful collaborationswith many mathematiciansfromvarious
countries.
In 1965, he went to Paris and attended Chevalley seminar. Of course
he met Grothendieck. Under the influence of the time, his first interest of
algebraic geometry was in a general aspect of the theory. Besides research
papers, he published his first book on algebraic geometry with Professors
M.NagataandM.Maruyamain1973.Thisbook wasthe firsttextbookon
a scheme theory available in Japanese language.
Professor Miyanishi continued his collaborations with mathematicians
likeProfessorsS. S.Abhyanker,P.RussellandR.V.Gurjar.Meanwhilehe
gradually shifted his interest towards concrete objects during the 70’s. He
isaleadingfigureinestablishinganewbranchofmathematicscalledaffine
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viii Dedication
algebraic geometry. He published more than 90 research articles and his
researchresultsonaffine algebraicgeometryinclude “Acharacterizationof
the affine plane”, “The cancellation problem of the affine plane” and “A
theoryoflogDel Pezzosurfaces”.His Tatalecture notesin1978is the first
summary of his researchin this area, and one of the good references of the
recent development in affine algebraic geometry is his article in the book
“Affine Algebraic Geometry, 2007 (T. Hibi, ed.)” published by the Osaka
University Press.
Apart from the activity on research and education, he made a great
contribution toward the university administration. He became a dean of
the faculty ofscience and afterwardswas a vice presidentof OsakaUniver-
sity until 2003. The time of his vice presidency corresponded to the time
when Japanese universities were preparing for corporatization. He played
an important role in performing this transition.
While he was a professor at Kwansei Gakuin University, he started a
conference on affine algebraic geometry at the Umeda campus of Kwansei
GakuinUniversityinMarch,2008.Heisstillgivingstimulationstoyounger
generations.
Toru Sugie
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PREFACE
A Conference on Affine Algebraic Geometry was held at Osaka Umeda
Campus of Kwansei Gakuin University during the period 3–6 March, 2011
ontheoccasionoftheseventiethbirthdayofProfessorMasayoshiMiyanishi.
Elevenresearcherswere invited from abroardand 19 talks were given. The
present proceedings is dedicated to Professor Miyanishi. This volume con-
tains16paperscontributedbyparticipantsintheconferenceandbyfriends
of Professor Miyanishi who were not able to participate in the conference.
All papers in this volume have been refereed. Most subjects treated in the
present volume are related to those Professor Miyanishi has been studying
and developing for more than 40 years.
Professor Miyanishi is one of the founders of affine algebraic geometry.
After the fundamental works by S. Abhyankar, M. Nagata and et al., he
laid the foundations in some of the theories of affine algebraic geometry.
Based on his deep and wide-ranged knowledge on algebraic geometry and
commutative algebra, he established the theory of open algebraic surfaces
withthepeopleincludingT.Fujita,S.Iitaka,Y.KawamataandS.Tsunoda.
He has authored 99 research papers so far. It is remarkable that he is
still very active after the retirement of the professorships he held in Osaka
UniversityandKwanseiGakuinUniversity.Indeed,heauthoredtenpapers
after his retirement from Kwansei Gakuin University which he had been
affiliatedtountillMarch,2009afterhavingleftOsakaUniversityin2003.He
isnowaguestresearcheroftheResearchCenterforMathematicalSciences,
which he himself established at Kwansei Gakuin University. As well as his
research, he has been devoted to the education. He brought up over ten
studentstoresearchers.Heisgenerousinsharingmathematicalideas.This
is testified by the fact that there are many joint papers with his colleagues
and students.
The conferencewasheldasthe 7thMeetingofAffineAlgebraicGeome-
try.The Affine AlgebraicGeometry Meeting has startedin March,2008as
a small meeting organized by Professor Miyanishi and me. Since then, the
meetinghasbeenheldtwiceayear,SeptemberandMarch,atOsakaUmeda
