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Volume 56 (2004)
- Issue 4 Pages 467-
- Issue 3 Pages 299-
- Issue 2 Pages 147-
- Issue 1 Pages 1-
Predecessor
Volume 56, Issue 4
Displaying 1-9 of 9 articles from this issue
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TETSU MASUDA2004 Volume 56 Issue 4 Pages 467-490
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSWe present a determinant expression for a family of classical transcendental solutions of the Painlevé V and the Painlevé VI equation. Degeneration of these solutions along the process of coalescence for the Painlevé equations is discussed.View full abstractDownload PDF (552K) -
XUESHAN ZHANG2004 Volume 56 Issue 4 Pages 491-499
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSIn 1973, Lawson and Simons conjectured that there are no stable currents in any compact, simply connected Riemannian manifold $M^m$ which is 1/4-pinched. In this paper, we regard $M^m$ as a submanifold immersed in a Euclidean space and prove the conjecture under some pinched conditions about the sectional curvatures and the principal curvatures of $M^m$. We also show that there is no stable $p$-current in a submanifold of $M^m$ and the $p$-th homology group vanishes when the shape operator of the submanifold satisfies certain conditions.View full abstractDownload PDF (480K) -
SHIGERU KURODA2004 Volume 56 Issue 4 Pages 501-522
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSWe generalize Roberts' counterexample to the fourteenth problem of Hilbert, and give a sufficient condition for certain invariant rings not to be finitely generated. It shows that there exist a lot of counterexamples of this type. We also determine the initial algebra of Roberts' counterexample for some monomial order.View full abstractDownload PDF (604K) -
SHIGEAKI MIYOSHI2004 Volume 56 Issue 4 Pages 523-530
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSThe Euler class, which lies in the second cohomology of the group of orientation preserving homeomorphisms of the circle, is pulled back to the “smooth” Euler class in the cohomology of the group of orientation preserving smooth diffeomorphisms of the circle. Suppose a surface group $\Gamma$ (of genus $>1$) is a normal subgroup of a group $G$, so that we have an extension of $Q = G/ \Gamma$ by $\Gamma$. We prove that if the canonical outer action of $Q$ on $\Gamma$ is finite, then there is a canonical second cohomology class of $G$ restricting to the Euler class on $\Gamma$ which is smoothly representable, that is, it is pulled back from the smooth Euler class by a representation from $G$ to the group of diffeomorphisms. Also, we prove that if the above outer action is infinite, then any second cohomology class of $G$ restricting to the Euler class on $\Gamma$ is not smoothly representable.View full abstractDownload PDF (480K) -
KATSUHISA MIMACHI, KATSUYOSHI OHARA, MASAAKI YOSHIDA2004 Volume 56 Issue 4 Pages 531-551
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSWe evaluate the intersection numbers of loaded cycles associated with an $n$-fold Selberg-type integral. We proceed inductively using high-dimensional local systems.View full abstractDownload PDF (558K) -
IRINA MARKINA2004 Volume 56 Issue 4 Pages 553-569
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSWe define the extremal length of horizontal vector measures on a Carnot group and study capacities associated with linear sub-elliptic equations. The coincidence between the definition of the $p$-module of horizontal vector measure system and two different definitions of the $p$-capacity is proved. We show the continuity property of a $p$-module generated by a family of horizontal vector measures. Reciprocal relations between the $p$-capacity and $q$-module $(1/p+1/q=1)$ of horizontal vector measures are obtained. A peculiarity of our approach consists of the study of the above mentioned notions in domains with an intrinsic metric.View full abstractDownload PDF (556K) -
KURT FALK, BERND O. STRATMANN2004 Volume 56 Issue 4 Pages 571-582
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSIn this paper we study normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), that are Kleinian groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set. We show that the limit set of a d-group always contains a range of fractal subsets, each containing the set of radial limit points and having Hausdorff dimension strictly less than the Hausdorff dimension of the whole limit set. We then consider normal subgroups $G$ of an arbitrary non-elementary Kleinian group $H$, and show that the exponent of convergence of $G$ is bounded from below by half of the exponent of convergene of $H$. Finally, we give a discussion of various examples of d-groups.View full abstractDownload PDF (513K) -
ALEXANDRU I. BADULESCU2004 Volume 56 Issue 4 Pages 583-592
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSDeligne, Kazhdan and Vignéras proved that, for an inner form of $GL_n$ over a zero characteristic $p$-adic field, the induced representation from a square integrable irreducible representation is irrreducible. Here we prove the case of non-zero characteristic.View full abstractDownload PDF (494K) -
PAOLO ALUFFI2004 Volume 56 Issue 4 Pages 593-619
Published: December 30, 2004
Released on J-STAGE: January 11, 2008
JOURNAL FREE ACCESSWe study different notions of blow-up of a scheme $X$ along a subscheme$Y$, depending on the datum of an embedding of $X$ into an ambient scheme. The two extremes in this theory are the ordinary blow-up, corresponding to the identity, and the ‘quasi-symmetric blow-up’, corresponding to the embedding of $X$ into a nonsingular variety. We prove that this latter blow-up is intrinsic of $Y$ and $X$, and is universal with respect to the requirement of being embedded as a subscheme of the ordinary blow-up of some ambient space along$Y$.
We consider these notions in the context of the theory of characteristic classes of singular varieties. We prove that if $X$ is a hypersurface in a nonsingular variety and $Y$ is its ‘singularity subscheme’, these two extremes embody respectively the conormal and characteristic cyclesof $X$. Consequently, the first carries the essential information computing Chern-Mather classes, and the second is likewise a carrier for Chern-Schwartz-MacPherson classes. In our approach, these classes are obtained from Segre class-like invariants, in precisely the same way as other intrinsic characteristic classes such as those proposed by Fulton, and by Fulton and Johnson.
We also identify a condition on the singularities of a hypersurface under which the quasi-symmetric blow-up is simply the linear fiber space associated with a coherent sheaf.View full abstractDownload PDF (611K)
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