Title: INT 97-22 NSF/Tokyo Report: US-Japan Seminar:
Classification of Algebraic Variables
Date: 6/3/97
The National Science Foundation's offices in Tokyo and in Paris periodically
report on developments abroad that are related to the Foundation's mission.
These documents present facts for the use of NSF program managers and policy
makers; they are not statements of NSF policy.
Special Scientific Report #97-16 (May 20, 1997)
The following report was submitted by Dr. Vyacheslav V. Shokurov, Professor of
Mathematics, The Johns Hopkins University, Baltimore, MD 21218. Dr. Shokurov,
in conjunction with, with Professor Yujiro Kawamata, Department of
Mathematical Sciences, University of Tokyo, Tokyo, Japan, helped organize a
U.S.-Japan joint seminar to discuss topics relating to the algebraic geometry.
The seminar was held April 9-10, 1997 in Baltimore, MD. The workshop was
jointly sponsored by NSF and the Japan Society for the Promotion of Science
(JSPS). This project is one of the joint projects supported under the
U.S.-Japan Cooperative Science Program. Dr. Shokurov can be reached via email
at: shokurov@math.jhu.edu
Professor Kawamata and I organized a collaborative activity at the Johns
Hopkins University on the classification of higher dimensional algebraic
varieties which coincided with the Algebraic Geometry year. A seminar on
higher dimensional algebraic geometry was held April 9-10, and an
international conference on birational geometry (in memory of Wei-Liang Chow)
followed from April 11-14. The former was partially supported by the NSF and
JSPS.
In view of the great importance of certain problems in this field, especially
the log minimal model problem, one of the main purposes of these two events
was to stimulate development of known approaches to solutions as well as
suggest new ones. We sponsored a series of visits by both Japanese and
American researchers to the Johns Hopkins University that culminated in the
U.S. - Japan seminar and international conference on birational geometry.
Leading European researchers also participated in the conference. This
program was one of the activities of the Japan-U.S. Mathematical Institute
(JAMI) that was established in 1988 at the Johns Hopkins University. The
importance of these events can be gauged from the schedule of presentations
and the list of participants that follows.
A volume with papers from Chow's conference will be published by the journal
Contemporary Mathematics.
List of Presentations:
SEMINAR/WORKSHOP
Tuesday, April 9
Y. Kachi, Flips from 4-folds with isolated complete intersection singularities
and the Pendant Tower." K. Matsuki, "Flops for 4-folds." N. Shepherd-Barron,
"Realizing finite Galois representations on Abelian varieties." F. Catanese,
"Homological algebra and algebraic surfaces." G. Xu, "On the intersections of
rational curves with cubic plane curves." V. Iskovskikh, "On rationality of
conic bundles."
Wednesday, April 10 S. Ishii, "Minimal, canonical and log-canonical models of
hypersurface singularities." H. Esnault, "Algebraic Chern-Simons theory." Y.
Miyaoka, "An effective version of a theorem of Bogomolov on curves on surfaces
of general type." K. Ohno, "Degeneration of surfaces with Kodaira dimension
zero." J. McKernan, "Effective k-cycles on the space of n-pointed rational
curves." A. Moriwaki, "A sharp slope inequality." M. Andreatta, "Extremal
contractions on smooth projective varieties."
CONFERENCE
Thursday, April 11 S. Abhyankar, "Fundamental groups of algebraic varieties."
F. Campana, "Remarks on the structure of the universal cover of compact
Kaehler manifolds." F. Bogomolov, "On the fundamental groups of projective
surfaces." Q. Zhang, "Projective manifolds with nef anticanonical bundles."
I. Nakamura, "Hilbert schemes and quotient singularities." J. Wahl,
"Hyperplane sections of Calabi-Yau varieties."
Friday, April 12 E. Viehweg, "Chow groups of projective varieties of very
small degree." V. Alexeev, "On complete moduli of abelian varieties." M.
Roczen, "Semi quasi homogeneous singularities of hypersurfaces with small
Saito invariant in positive characteristics." A. Sommese, "Numerical algebraic
geometry." S. Kovacs, "Vanishing and isotriviality for families."
Saturday, April 13 N. Nakayama, "Global structure of an elliptic fibration."
S. Mukai, "Gorenstein Fano 3-folds." M. Beltrametti, "On the adjunction
mapping--The very ampleness of the triadjoint bundle." P.M.H. Wilson,
"Calabi-Yaus as symplectic manifolds." K. Oguiso, "Calabi-Yau threefolds of
quasi-product type." Y. Namikawa, "Deformation theory of Calabi-Yau threefolds
with singularities."
Sunday, April 14 A. Borisov, "Boundedness problems for Fano varieties with
singularities." D. Morrison, "Fibered Calabi-Yau manifolds and new dualities
in string theory." M. Gross, "Primitive Calabi-Yau threefolds."