Recursos de colección
Kitadai, Yukinori; Sumihiro, Hideyasu
We 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 $K_X$.
Hauswirth, Laurent; Sa Earp, Ricardo; Toubiana, Eric
We 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...
Li, Zhenyang; Shi, Yuguang
We 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.
Murase, Atsushi; Narita, Hiro-aki
T. Arakawa, in his unpublished note, constructed and studied a theta lifting from elliptic cusp forms to automorphic forms on the quaternion unitary group of signature $(1, q)$.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...
Øbro, Mikkel
We 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.
Suwa, Noriyuki
We 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.
Thorbergsson, Gudlugur; Umehara, Masaaki
A 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...
Asada, Mamoru
We 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.
Alessandrini, Lucia; Bassanelli, Giovanni
We 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.
Cheng, Xu; Cheung, Leung-fu; Zhou, Detang
We 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 $H$.
Fujisawa, Taro
We 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.
Guo, Jong-Shenq; Wu, Chin-Chin
We 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.
Sasaki, Takeshi; Yoshida, Masaaki
By 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 ${\rm
GL}(2,\boldsymbol{R})$-action extending the Markoff transformations.
Calabri, Alberto; Lopes, Margarida Mendes; Pardini, Rita
Numerical 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.
Namba, Makoto
Furumochi, Tetsuo
Nishikawa, Seiki
Takagi, Hitoshi
Tanno, Shükichi
Takemoto, Hideo