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Volume 60 (2008)
- Issue 4 Pages 459-
- Issue 3 Pages 303-
- Issue 2 Pages 149-
- Issue 1 Pages 1-
Predecessor
Volume 60, Issue 1
Displaying 1-7 of 7 articles from this issue
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ALBERTO CALABRI, MARGARIDA MENDES LOPES, RITA PARDINI2008 Volume 60 Issue 1 Pages 1-22
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSNumerical Campedelli surfaces are minimal surfaces of general type with vanishing geometric genus and canonical divisor with self-intersection 2. Although they have been studied by several authors, their complete classification is not known.
In this paper we classify numerical Campedelli surfaces with an involution, i.e., an automorphism of order 2. First we show that an involution on a numerical Campedelli surface $S$ has either four or six isolated fixed points, and the bicanonical map of $S$ is composed with the involution if and only if the involution has six isolated fixed points. Then we study in detail each of the possible cases, describing also several examples.View full abstractDownload PDF (211K) -
TAKESHI SASAKI, MASAAKI YOSHIDA2008 Volume 60 Issue 1 Pages 23-36
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSBy the Fricke surfaces, we mean the cubic surfaces defined by the equation $p^2+q^2+r^2-pqr-k=0$ in the Euclidean 3-space with the coordinates $(p,q,r)$ parametrized by constant $k$. When $k=0$, it is naturally isomorphic to the moduli of once-punctured tori. It was Markoff who found the transformations, called Markoff transformations, acting on the Fricke surface. The transformation is typically given by $(p,q,r)\mapsto (r,q,rq-p)$ acting on $\boldsymbol{R}^3$ that keeps the surface invariant. In this paper we propose a way of interpolating the action of Markoff transformation. As a result, we show that one portion of the Fricke surface with $k=4$ admits a $\textrm{GL}(2,\boldsymbol{R})$-action extending the Markoff transformations.View full abstractDownload PDF (272K) -
JONG-SHENQ GUO, CHIN-CHIN WU2008 Volume 60 Issue 1 Pages 37-70
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSWe study the solution of the heat equation with a strong absorption. It is well-known that the solution develops a dead-core in finite time for a large class of initial data. It is also known that the exact dead-core rate is faster than the corresponding self-similar rate. By using the idea of matching, we formally derive the exact dead-core rates under a dynamical theory assumption. Moreover, we also construct some special solutions for the corresponding Cauchy problem satisfying this dynamical theory assumption. These solutions provide some examples with certain given polynomial rates.View full abstractDownload PDF (238K) -
TARO FUJISAWA2008 Volume 60 Issue 1 Pages 71-100
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSWe introduce the notion of a log smooth degeneration, which is a logarithmic analogue of the central fiber of some kind of degenerations of complex manifolds over polydiscs. Under suitable conditions, we construct a natural cohomological mixed Hodge complex on the reduction of a compact log smooth degeneration. In particular, we obtain mixed Hodge structures on the log de Rham cohomologies and $E_1$-degeneration of the log Hodge to de Rham spectral sequence for a certain kind of compact reduced log smooth degenerations.View full abstractDownload PDF (233K) -
XU CHENG, LEUNG-FU CHEUNG, DETANG ZHOU2008 Volume 60 Issue 1 Pages 101-121
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSWe study the global behavior of weakly stable constant mean curvature hypersurfaces in a Riemannian manifold by using harmonic function theory. In particular, a complete oriented weakly stable minimal hypersurface in the Euclidean space must have only one end. Any complete noncompact weakly stable hypersurface with constant mean curvature $H$ in the 4 and 5 dimensional hyperbolic spaces has only one end under some restrictions on $H$.View full abstractDownload PDF (167K) -
LUCIA ALESSANDRINI, GIOVANNI BASSANELLI2008 Volume 60 Issue 1 Pages 123-134
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSWe define on a manifold $X$ a wedge product $S \wedge T$ of a closed positive $(1,1)$-current $S$, smooth outside a proper analytic subset $Y$ of $X$, and a positive pluriharmonic $(k,k)$-current $T$, when $k$ is less than the codimension of $Y$. Using this tool, we prove that if $M$ is a compact complex manifold of dimension $n \geq 3$, which is Kähler outside an irreducible curve, then $M$ carries a balanced metric.View full abstractDownload PDF (130K) -
MAMORU ASADA2008 Volume 60 Issue 1 Pages 135-147
Published: March 30, 2008
Released on J-STAGE: May 10, 2011
JOURNAL FREE ACCESSWe shall consider the maximal cyclotomic extension of a finite algebraic number field and its two abelian extensions, the maximal abelian extension and the maximal abelian extension with certain restricted ramification. We shall investigate the structure of these Galois groups with the action of the cyclotomic Galois group.View full abstractDownload PDF (135K)
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