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Volume 39 (2003)
- Issue 4 Pages 625-
- Issue 3 Pages 435-
- Issue 2 Pages 205-
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Volume 39, Issue 4
Displaying 1-7 of 7 articles from this issue
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Fumio Hazama2003 Volume 39 Issue 4 Pages 625-655
Published: 2003
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSThe General Hodge Conjecture for abelian varieties of CM-type is shown to be implied by the usual Hodge Conjecture for those up to codimension two.View full abstractDownload PDF (281K) -
Kunio Ichinobe2003 Volume 39 Issue 4 Pages 657-693
Published: 2003
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe shall develop the theory of Borel summability or k-summability for a divergent solution of the Cauchy problem for non-Kowalevskian equations of quasi-homogeneous type. Precisely, we first establish necessary and sufficient conditions for the Borel summability in terms of the Cauchy data (cf. Theorem 2.1), and next we give an integral representation of the Borel sum by using kernel functions which are given by Meijer G-function or the generalized hypergeometric functions of confluent type (cf. Theorems 2.3 and 2.6).View full abstractDownload PDF (308K) -
Hidekazu Furusho2003 Volume 39 Issue 4 Pages 695-720
Published: 2003
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSThe MZV algebra is the graded algebra over Q generated by all multiple zeta values. The stable derivation algebra is a graded Lie algebra version of the Grothendieck-Teichmüller group. We shall show that there is a canonical surjective Q-linear map from the graded dual vector space of the stable derivation algebra over Q to the new-zeta space, the quotient space of the sub-vector space of the MZV algebra whose grade is greater than 2 by the square of the maximal ideal. As a corollary, we get an upper-bound for the dimension of the graded piece of the MZV algebra at each weight in terms of the corresponding dimension of the graded piece of the stable derivation algebra. If some standard conjectures by Y. Ihara and P. Deligne concerning the structure of the stable derivation algebra hold, this will become a bound conjectured in Zagier's talk at 1st European Congress of Mathematics. Via the stable derivation algebra, we can compare the new-zeta space with the l-adic Galois image Lie algebra which is associated with the Galois representation on the pro-l fundamental group of P\frac{1}{Q}−{0, 1, ∞}.View full abstractDownload PDF (289K) -
Michael Finkelberg, Dennis Gaitsgory, Alexander Kuznetsov2003 Volume 39 Issue 4 Pages 721-766
Published: 2003
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSWe introduce an Uhlenbeck closure of the space of based maps from projective line to the Kashiwara flag scheme of an untwisted affine Lie algebra. For the algebra \widehat{sl}n this space of based maps is isomorphic to the moduli space of locally free parabolic sheaves on P1×P1 trivialized at infinity. The Uhlenbeck closure admits a resolution of singularities: the moduli space of torsion free parabolic sheaves on P1×P1 trivialized at infinity. We compute the Intersection Cohomology sheaf of the Uhlenbeck space using this resolution of singularities. The moduli spaces of parabolic sheaves of various degrees are connected by certain Hecke correspondences. We prove that these correspondences define an action of \widehat{sl}n in the cohomology of the above moduli spaces.View full abstractDownload PDF (489K) -
Toshiko Ogiwara, Ken-Ichi Nakamura2003 Volume 39 Issue 4 Pages 767-783
Published: 2003
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSThis paper is concerned with nonlinear diffusion equations related to a model of the motion of screw dislocations on crystal surfaces. We prove the existence, uniqueness and asymptotic stability of a rotating and growing solution with a time-independent profile, which we call a spiral traveling wave solution.View full abstractDownload PDF (206K) -
Kenta Kobayashi2003 Volume 39 Issue 4 Pages 785-796
Published: 2003
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSWe propose an improvement on the Fast Gauss Transform which was presented by Greengard and Sun [Documenta Mathematica, Extra volume ICM 1998, III, pp.575–584 (1998)]. In their method, plane waves are used to approximate the Gauss kernel. Plane waves they used were generated by the Fourier integral and the trapezoidal rule. We propose different plane waves, which enables us to calculate the Fast Gauss Transform more efficiently.View full abstractDownload PDF (139K) -
Tristan Torrelli2003 Volume 39 Issue 4 Pages 797-822
Published: 2003
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSLet f, g be two germs of holomorphic functions on Cn such that f is smooth at the origin and (f, g) defines an analytic complete intersection (Z, 0) of codimension two. We study Bernstein polynomials of f associated with sections of the local cohomology module with support in X=g−1(0), and in particular some sections of its minimal extension. When (X, 0) and (Z, 0) have an isolated singularity, this may be reduced to the study of a minimal polynomial of an endomorphism on a finite dimensional vector space. As an application, we give an effective algorithm to compute those Bernstein polynomials when f is a coordinate and g is non-degenerate with respect to its Newton boundary.View full abstractDownload PDF (300K)
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