Koji Cho

Uniqueness and Examples of Compact Toric Sasaki-Einstein Metrics

In [11] it was proved that, given a compact toric Sasaki manifold with positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on

DIFFERENTIAL STRUCTURE OF ABELIAN FUNCTIONS

S^5 sharp k(S^2 times S^3)

Veronese arrangements of hyperplanes in real projective spaces

for each positive integer k.

Baker-Akhiezer modules on the intersections of shifted theta divisors

The beta function B(α, β ) is defined by the following integral where arg , and the gamma function Γ(β ) by where arg .

COMPARISON OF (CO)HOMOLOGIES OF BRANCHED COVERING SPACES AND TWISTED ONES OF BASESPACES I

The space of Abelian functions of a principally polarized abelian variety (J,Θ) is studied as a module over the ring of global holomorphic differential operators on J. We construct a free resolution in case Θ is non-singular. As an application, in the case of dimensions 2 and 3, we construct a new linear basis of the space of abelian functions which are singular only on Θ in terms of logarithmic derivatives of the higher-dimensional σ-function.

A HYPERGEOMETRIC INTEGRAL ATTACHED TO THE CONFIGURATION OF THE MIRRORS OF THE REFLECTION GROUP Sn+2 ACTING ON Pn

The asymptotic behavior at infinity of oscillatory integrals is in detail investigated by using the Newton polyhedra of the phase and the amplitude. We are especially interested in the case that the amplitude has a zero at a critical point of the phase. The properties of poles of local zeta functions, which are closely related to the behavior of oscillatory integrals, are also studied under the associated situation.

Combinatorial structure of the configuration space of 6 points on the projective plane

This paper studies chambers cut out by a special kind of hyperplane arrangements in general position, the Veronese arrangements, in the real projective spaces.

Six points / planes in the 3-space

The restriction, on the spectral variables, of the Baker-Akhiezer (BA) module of a g-dimensional principally polarized abelian variety with the non-singular theta divisor to an intersection of shifted theta divisors is studied. It is shown that the restriction to a k-dimensional variety becomes a free module over the ring of differential operators in