Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor
ISHII Akira
Degree 1
-
博士（理学） （ 2000.1 京都大学 ）
Papers 17
-
G-constellations and the maximal resolution of a quotient surface singularity Reviewed
Ishii Akira
HIROSHIMA MATHEMATICAL JOURNAL Vol. 50 ( 3 ) page： 375 - 398 2020.11
-
Extended McKay correspondence for quotient surface singularities Reviewed
Akira Ishii, Iku Nakamura
The Quarterly Journal of Mathematics Vol. 70 ( 2 ) page： 395 - 408 2019.6
-
Dimer models and crepant resolutions Reviewed
Akira Ishii, Kazushi Ueda
Hokkaido Math. J. Vol. 45 ( 1 ) page： 1--42 2016
-
Dimer models and the special McKay correspondence Reviewed
Akira Ishii, Kazushi Ueda
Geom. Topol. Vol. 19 ( 6 ) page： 3405--3466 2015
-
The special McKay correspondence and exceptional collections Reviewed
Akira Ishii, Kazushi Ueda
Tohoku Math. J. Vol. 67 ( 4 ) page： 585--609 2015
-
On G/N-Hilb of N-Hilb Reviewed
Akira Ishii, Álvaro Nolla de Celis, Yukari Ito
Kyoto J. Math. Vol. 53 ( 1 ) page： 91--130 2013
-
A note on derived categories of Fermat varieties Reviewed
Akira Ishii, Kazushi Ueda
Derived categories in algebraic geometry, EMS Ser. Congr. Rep. page： 103--110 2012
-
A note on consistency conditions on dimer models Reviewed
Akira Ishii, Kazushi Ueda
RIMS Kôkyûroku Bessatsu Vol. B24 page： 143--164 2011
-
Stability conditions on An-singularities Reviewed
Akira Ishii, Kazushi Ueda, Hokuto Uehara
J. Differential Geom. Vol. 84 ( 1 ) page： 87--126 2010
-
On moduli spaces of quiver representations associated with dimer models. Reviewed
Akira Ishii and Kazushi Ueda
RIMS Kôkyûroku Bessatsu Vol. B9 page： 127--141 2008
-
Autoequivalences of derived categories on the minimal resolutions of An-singularities on surfaces. Reviewed
Akira Ishii, Hokuto Uehara
J. Differential Geom. Vol. 71 ( 3 ) page： 385--435 2005
-
Representation moduli of the McKay quiver for finite abelian subgroups of SL(3,C). Reviewed
Akira Ishii
Clay Math. Proc. Vol. 3 page： 227--237 2004
-
Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient. Reviewed
Akira Ishii, Alastair Craw
Duke Math. J. Vol. 124 ( 2 ) page： 259--307 2004
-
On the McKay correspondence for a finite small subgroup of GL(2,C) Reviewed
Akira Ishii
J. Reine Angew. Math. Vol. 549 page： 221--233 2002
-
Versal deformation of reflexive modules over rational double points Reviewed
Akira Ishii
Math. Ann. Vol. 317 ( 2 ) page： 239--262 2000
-
Semi-universal family of reflexive modules over a rational double point of type A Reviewed
Akira Ishii
Lecture Notes in Pure and Appl. Math. Vol. 179 page： 65--77 1996
-
On the moduli of reflexive sheaves on a surface with rational double points Reviewed
Akira Ishii
Math. Ann. Vol. 294 ( 1 ) page： 125--150 1992
KAKENHI (Grants-in-Aid for Scientific Research) 3
-
McKay correspondence and derived category
Grant number：19K03444 2019.4 - 2022.3
Authorship：Principal investigator
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
-
Existence of higher dimensional crepant resolutions and generlization of the McKay correspondence
Grant number：18K03209 2018.4 - 2023.3
Authorship：Coinvestigator(s)
-
Singularities and derived catetories
Grant number：15K04819 2015.4 - 2019.3
Ishii Akira
Authorship：Principal investigator
Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）
(1) We studied some globalisation of the so-called special McKay correspondence for a two-dimensional quotient singularity with Iku Nakamura and obtained a description of it.
(2) For a two-dimensional quotient singularity, we characterized those resolutions dominated by the so-called maximal resolution as the moduli spaces of G-constellations.
(3) We studied dimer models with group actions with Alvaro Nolla and Kazushi Ueda and constructed non-commutative crepant resolutions of the quotient of an affine topic variety by the symmetry of a lattice polygon.