1.
On Non-existenceness of Equifocal Submanifolds with Non-flat Section - Koike, Naoyuki
We first prove a certain kind of splitting theorem for an equifocal submanifold
with non-flat section in a simply connected symmetric space of compact type, where an equifocal
submanifold means a submanifold with parallel focal structure. By using the splitting theorem,
we prove that there exists no equifocal submanifold with non-flat section in an irreducible simply
connected symmetric space of compact type whose codimension is greater than the maximum of
the multiplicities of roots of the symmetric space or the maximum added one. In particular, it
follows that there exists no equifocal submanifold with non-flat section in some irreducible simply
connected symmetric spaces of compact type and...
5.
Localization, Hurwitz Numbers and the Witten Conjecture - Chen, Lin; Li, Yi; Liu, Kefeng
In this note, we use the combinatorial method of Goulden-Jackson-Vakil to give a
simple proof of Witten conjecture-Kontsevich theorem.
7.
Topology of Co-symplectic/Co-Kähler Manifolds - Li, Hongjun
Co-symplectic/co-Kähler manifolds are odd dimensional analog of symplectic/Kähler
manifolds, defined early by Libermann in 1959/Blair in 1967 respectively. In this paper, we reveal
their topology construction via symplectic/Kähler mapping tori. Namely,
Theorem. Co-symplectic manifold = Symplectic mapping torus;
Co-Kähler manifold = Kähler mapping torus.
9.
Preface
This is the special issue dedicated to Professor Yum-Tong Siu on the
occasion of his 60th birthday.
10.
GLOBAL SOLUTIONS OF EINSTEIN-DIRAC EQUATION - LU
, QIKENG; WANG
, SHIKUN; WU
, KE
The conformal space \frac M was introduced by Dirac in 1936. It is an algebraic manifold
with a spin structure and possesses naturally an invariant Lorentz metric. By carefully studying the
birational transformations of \frac M, we obtain explicitly the transition functions of the spin bundle over
\frac M. Since the transition functions are closely related to the propagation in physics, we get a kind of
solutions of the Dirac equation by integrals constructed from the propagation. Moreover, we prove
that the invariant Lorentz metric together with one of such solutions satisfies the Einstein-Dirac
combine equation
11.
IRREGULAR MANIFOLDS WHOSE CANONICAL SYSTEM
IS COMPOSED OF A PENCIL - CAI
, JIN-XING; VIEHWEG
, ECKART
Let X be a complex projective n-dimensional manifold of general type whose canonical
system is composite with a pencil. If the Albanese map is generically finite, but not surjective,
or if the irregularity is strictly larger than n and the image of X in Alb(X) is of Kodaira dimension
one, then the geometric genus pg(F) of a general fibre F of the canonical map is one and the latter
factors through the Albanese map. The last part of this result holds true for any threefold with
q(X) ? 5.
12.
THE EINSTEIN KÄHLER METRIC WITH EXPLICIT FORMULAS
ON SOME NON-HOMOGENEOUS DOMAINS - WANG
, AN; YIN
, WEIPING; ZHANG
, LIYOU; ZHANG
, WENJUAN
In this paper we describe the Einstein-Kähler metric for the Cartan-Hartogs domains
which are the special case of the Hua domains. First of all, we reduce the Monge-Ampére equation
for the metric to an ordinary differential equation in the auxiliary function X = X(z,w). This
differential equation can be solved to give an implicit function in X. Secondly, for some cases, we
obtained explicit forms of the complete Einstein-Kähler metrics on Cartan-Hartogs domains which
are the non-homogeneous domains.
13.
BIRATIONALITY OF THE TANGENT
MAP FOR MINIMAL RATIONAL CURVES - HWANG
, JUN-MUK; MOK
, NGAIMING
For a uniruled projective manifold, we prove that a general rational curve of minimal
degree through a general point is uniquely determined by its tangent vector. As applications, among
other things we give a new proof, using no Lie theory, of our earlier result that a holomorphic map
from a rational homogeneous space of Picard number 1 onto a projective manifold different from the
projective space must be a biholomorphic map.
14.
VANISHING COHOMOLOGY FOR HOLOMORPHIC
VECTOR BUNDLES IN A BANACH SETTING - LEMPERT
, LÁSZLÓ
For a large class of Banach spaces X we prove the following. If ? ? X is open and
pseudoconvex, and E ? ? is a locally trivial holomorphic Banach bundle, then the sheaf cohomology
groups Hq(?, E) vanish for q ? 1. We also give an application concerning
neighborhoods of complex
submanifolds.
17.
A REMARK ON THE DOUADY SEQUENCE
FOR NON-PRIMARY HOPF MANIFOLDS - ZHOU
, XIANG-YU
To determine cohomology groups of holomorphic vector bundles
or more general coherent analytic sheaves on complex manifolds is very important
in several complex variables and complex geometry. For example, Cartan-Serre's theorem
B and Kodaira's vanishing theorem are fundamental respectively in the studies of
two classes of complex manifolds: Stein manifolds and projective algebraic manifolds.
Deformation and moduli space of complex structures are also closely related to the determination
of the cohomology groups of the bundles according to Kodaira-Spencer's
theory
18.
REAL AND COMPLEX HAMILTONIAN MECHANICS ON SOME
SUBRIEMANNIAN MANIFOLDS - CALIN
, OVIDIU; CHANG
, DER-CHEN; GREINER
, PETER
We prove geodesic completeness and global conectivity for a step 2k + 2 subRiemannian
manifold. Using complex Hamiltonian mechanics we also calculate some subRiemannian
distances.
19.
CUBIC EQUATIONS FOR THE HYPERELLIPTIC LOCUS - GRUSHEVSKY
, SAMUEL
We prove a conjecture from [BK2] that the multi-dimensional vector addition formula
for Baker-Akhiezer functions obtained there characterizes Jacobians among principally polarized
abelian varieties. We also show that this addition formula is equivalent to Gunning's multisecant
formula for the Kummer variety obtained in [Gu2].
¶
We then use this addition formula to obtain cubic relations among theta functions that characterize
the locus of hyperelliptic Jacobians among irreducible abelian varieties. In genus 3 our equations
are equivalent to the vanishing of one theta-null, and thus are classical (see [M], [P]), but already for
genus 4 they appear to be new.
20.
INTEGRATION OF MEROMORPHIC COHOMOLOGY CLASSES
AND APPLICATIONS - BARLET
, DANIEL; MAGNÚSSON
, JON
The main purpose of this article is to increase the efficiency of the tools introduced in
[B.Mg. 98] and [B.Mg. 99], namely integration of meromorphic cohomology classes, and to generalize
the results of [B.Mg. 99]. They describe how positivity conditions on the normal bundle of a compact
complex submanifold Y of codimension n + 1 in a complex manifold Z can be transformed into
positivity conditions for a Cartier divisor in a space parametrizing n-cycles in Z .
¶
As an application of our results we prove that the following problem has a positive answer in
many cases :
¶
Let Z be a compact connected complex manifold of...
1.
