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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 2
Displaying 1-7 of 7 articles from this issue
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GUDLAUGUR THORBERGSSON, MASAAKI UMEHARA2008 Volume 60 Issue 2 Pages 149-181
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSA simple closed curve in the real projective plane is called anti-convex if for each point on the curve, there exists a line which is transversal to the curve and meets the curve only at that given point. Our main purpose is to prove an identity for anti-convex curves that relates the number of independent (true) inflection points and the number of independent double tangents on the curve. This formula is a refinement of the classical Möbius theorem. We also show that there are three inflection points on a given anti-convex curve such that the tangent lines at these three inflection points cross the curve only once. Our approach is axiomatic and can be applied in other situations. For example, we prove similar results for curves of constant width as a corollary.View full abstractDownload PDF (395K) -
NORIYUKI SUWA2008 Volume 60 Issue 2 Pages 183-218
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSWe discuss an analogue of the Kummer and Kummer-Artin-Schreier theories, twisting by a quadratic extension. The argument is developed not only over a field but also over a ring, as generally as possible.View full abstractDownload PDF (222K) -
MIKKEL ØBRO2008 Volume 60 Issue 2 Pages 219-225
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSWe examine a concrete smooth Fano 5-polytope $P$ with 8 vertices with the following properties: There does not exist a smooth Fano 5-polytope $Q$ with 7 vertices such that $P$ contains $Q$, and there does not exist a smooth Fano 5-polytope $R$ with 9 vertices such that $R$ contains $P$. As the polytope $P$ is not pseudo-symmetric, it is a counter example to a conjecture proposed by Sato.View full abstractDownload PDF (77K) -
ATSUSHI MURASE, HIRO-AKI NARITA2008 Volume 60 Issue 2 Pages 227-251
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESST. Arakawa, in his unpublished note, constructed and studied a theta lifting from elliptic cusp forms to automorphic forms on the quaternion unitary group of signature $(1,q)$. The second named author proved that such a lifting provides bounded (or cuspidal) automorphic forms generating quaternionic discrete series. In this paper, restricting ourselves to the case of $q=1$, we reformulate Arakawa's theta lifting as a theta correspondence in the adelic setting and determine a commutation relation of Hecke operators satisfied by the lifting. As an application, we show that the theta lift of an elliptic Hecke eigenform is also a Hecke eigenform on the quaternion unitary group. We furthermore study the spinor $L$-function attached to the theta lift.View full abstractDownload PDF (197K) -
ZHENYANG LI, YUGUANG SHI2008 Volume 60 Issue 2 Pages 253-265
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSWe prove the existence of maximal slices in anti-de Sitter spaces (ADS spaces) with small boundary data at spatial infinity. The main argument is carried out by implicit function theorem. We also get a necessary and sufficient condition for the boundary behavior of totally geodesic slices in ADS spaces. Moreover, we show that any isometric and maximal embedding of hyperbolic spaces into ADS spaces must be totally geodesic. Combined with this, we see that most of maximal slices obtained in this paper are not isometric to hyperbolic spaces, which implies that the Bernstein Theorem in ADS space fails.View full abstractDownload PDF (119K) -
LAURENT HAUSWIRTH, RICARDO SA EARP, ERIC TOUBIANA2008 Volume 60 Issue 2 Pages 267-286
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSWe establish the definition of associate and conjugate conformal minimal isometric immersions into the product spaces, where the first factor is a Riemannian surface and the other is the set of real numbers. When the Gaussian curvature of the first factor is nonpositive, we prove that an associate surface of a minimal vertical graph over a convex domain is still a vertical graph. This generalizes a well-known result due to R. Krust. Focusing the case when the first factor is the hyperbolic plane, it is known that in certain class of surfaces, two minimal isometric immersions are associate. We show that this is not true in general. In the product ambient space, when the first factor is either the hyperbolic plane or the two-sphere, we prove that the conformal metric and the Hopf quadratic differential determine a simply connected minimal conformal immersion, up to an isometry of the ambient space. For these two product spaces, we derive the existence of the minimal associate family.View full abstractDownload PDF (221K) -
YUKINORI KITADAI, HIDEYASU SUMIHIRO2008 Volume 60 Issue 2 Pages 287-301
Published: June 30, 2008
Released on J-STAGE: July 15, 2011
JOURNAL FREE ACCESSWe study the stability of direct images by Frobenius morphisms. First, we compute the first Chern classes of direct images of vector bundles by Frobenius morphisms modulo rational equivalence up to torsions. Next, introducing the canonical filtrations, we prove that if $X$ is a nonsingular projective minimal surface of general type with semistable $\Omega_X^1$ with respect to the canonical line bundle $K_X$, then the direct images of line bundles on $X$ by Frobenius morphisms are semistable with respect to $K_X$.View full abstractDownload PDF (145K)
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