Kollar, J. / Mori Shigefumi :
Birational Geometry of Algebraic Varieties
One of the major discoveries of the last two decades in
algebraic geometry is the realization that
the theory of minimal models of surfaces can be generalized to
higher dimensional varieties.
This generalization, called the minimal model program or Mori's
program, has developed into a powerful tool with applications to
diverse questions in algebraic geometry and beyond.
This book provides the first comprehensive introduction to the
circle of ideas developed around the program, the prerequisites
begin only a basic knowledge of algebraic geometry.
It will be of great interest to graduate students and researchers
working in algebraic geometry and related fields.
Oct. 1998 320 pp.
0-521-63277-3
Recent Title in the Series
Vol. 135:
Miwa, T. / Jimbo, M. / Date, E. : Mathematics of Solitons
Sep. 1998 180 pp. 0-521-56161-2
Cambridge
Katz, N. / Sarnak, P. :
Random Matrices, Frobenius Eigenvalues, and Monodromy
The main topic of this book is the deep relation between the
spacings between zeros of zeta and L-functions and spacings
between eigenvalues of random elements of large compact classical
groups. This relation, the Montgomery-Odlyzko law, is shown to
hold for wide classes of zeta and L-functions over finite fields.
The book draws on, and gives accessible accounts of, many
disparate areas of mathematics, from algebraic geometry, moduli
spaces, monodromy, equidistribution, and Weil conjectures, to
probability theory on the compact classical groups in the limit
as their dimension goes to infinity and related techniques from
orthogonal polynomials and Fredholm determinants.
1998 416 pp.
0-8218-1017-0
A.M.S.
Knus, M.-A. /Merkurjev, A. /Tignol, J.-P.:
The Book Involutions
This monograph is an exposition of the theory of central simple
algebras with involution, in relation to linear algebraic groups.
It provides the algebra-theoretic foundations for much of the recent work
on linear algebraic groups over arbitrary fields.
Involutions are viewed as twisted forms of (hermitian) quadrics,
leading to new developments on the model of the algebraic theory of quadratic forms.
In addition to classical groups, phenomena related to triality are also discussed,
as well as groups of type F4 or G2 arising from exceptional Jordan or composition algebras.
Several results and notions appear here for the first time,
notably the discriminant algebra of an algebra with unitary involution
and the algebra-theoretic counterpart to linear groups of type D4.
Aug. 1998 593 pp.
0-8218-0904-0
A. M. S.
Everitt, N. /Markus, L. :
Boundary Value Problems and Symplectic Algebra for Ordinary
Differential and Quasi-differential Operators
In the classical theory of self-adjoint boundary value problems for
linear ordinary differential operators there is a fundamental,
but rather mysterious, interplay between the symmetric (conjugate)
bilinear scalar product of the basic Hilbert space and the skew-symmetric boundary
form of the associated differential expression.
1998 200 pp.
0-8218-1080-4 9,750.
A. M. S.
Aubin, T. :
Some Nonlinear Problems in Riemannian Geometry
A very interesting area of nonlinear partial differential
equations lies in the study of special equations arising in
Geometry and Physics. This book deals with such important
subjects as variational method, parabolic equations on fiber
bundles, ideas concerning points of concentration, blowing-up
technique, geometric and topological methods.
... 1998 350 pp.
3-540-60752-8
Springer
Ivrii, V. :
Microlocal Analysis and Precise Spectral Asymptotics
Devoted to the methods of microlocal analysis applied to
spectral asymptotics with accurate remainder estimates, this long
awaited book develops the very powerful machinery of local and
microlocal semiclassical spectral asymptotics, as well as methods
of combining these asymptotics with spectral estimates. The
rescaling technique, an easy to use and very powerful tool, is
presented. Many theorems, considered till now as independent and
difficult, are now just special cases of easy corollaries of the
theorems proved in this book. Most of the results and their
proofs are as yet unpublished.
... 1998 752 pp.
3-540-62780-4
Springer
Griess, Jr. R.:
Twelve Sporadic Groups
The finite simple groups come in several infinite families
(alternating groups and the groups of Lie type) plus 26 sporadic groups.
The sporadic groups, discovered between 1861 and 1975,
exist because of special combinatorial or arithmetic circumstances.
A single theme does not capture them all.
Nevertheless, certain themes dominate.
The 20 sporadics involved in the Monster, the largest sporadic group,
constitute the Happy Family.
A leisurely and rigorous study of two of their three generations is
the purpose of this book.
... 1998 200 pp.
3-540-62780-4
Recent Titles in the Series
Abhyankar, S. :
Resolution of Singularities of Embedded ALgebraic Surfaces, 2nd ed.
Elstrodt, J. /Grunewald, F. / Mennicke, J. :
Groups Acting on Hyperbolic Space
Rudyak, Yu, B. :
On Thom Spectra Orientabiity and Cobordism
Springer
Morimoto Mitsuo :
Analytic Functionals on the Sphere:
Analytic Functionals on the Sphere
This book treats spherical harmonic expansion of real
analytic functions and hyperfunctionson the sphere. Because a
one-dimensional sphere is a circle, the simplest example of the
theory is that of Fourier series of periodic functions. The
author first introduces a system of complex neighborhoods of the
sphere by means of the Lie norm. He then studies holomorphic
functions and analytic functionals on the complex sphere. In the
one-dimensional case, this corresponds to the study of
holomorphic functions and analytic functionals on the annular set
in the complex plane, relying on the Laurent series expansion. In
this volume, it is shown that the same idea still works in a
higher-dimensional sphere.
Sep. 1998 170 pp.
0-8218-0585-1
A.M.S.
Voskresenskii, V. E. :
Algebraic Groups and Their Birational Invariants
Since the late 1960s, methods of birational geometry have been used
successfully in the theory of linear algebraic groups, especially in arithmetic problems.
This book--which can be viewed as a significant revision of the author's book,
Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties
of linear algebraic groups focusing on arithmetic applications.
The main topics are forms and Galois cohomology,
the Picard group and the Brauer group,
birational geometry of algebraic tori,
arithmetic of algebraic groups, Tamagawa numbers,
R-equivalence, projective toric varieties,
invariants of finite transformation groups,
and index-formulas.
Sep. 1998 227 pp.
0-8218-0905-9
A. M. S.
Fillmore, p. / Mingo, J. :
Operator Algebras and Their Applications, II
The study of operator algebras, which grew out of von Neumann's work in the 1920s and 30s
on modelling quantum mechanics, has in recent years experienced tremendous growth and
vitality, with significant applications in
other areas both within mathematics and in other fields.
This volume is the second selection of papers that arose from
the seminars and workshops of a year-long program, Operator Algebras and Applications,
that took place at The Fields Institute.
1998 170 pp.
0-8218-0908-3
A. M. S.