106,070 research outputs found
On surfaces of general type with maximal Albanese dimension
Given a minimal surface equipped with a generically finite map to an Abelian
variety, we give an optimal bound on the canonical degree of a rational or an
elliptic curve. As a corollary, we obtain the finiteness of rational and
elliptic curves on any surface of general type with two linearly independent
regular one forms.Comment: 13 page
A refined Kodaira dimension and its canonical fibration
Given a (meromorphic) fibration where and are compact
complex manifolds of dimensions and , we define to be the
invertible subsheaf of the sheaf of holomorphic -forms of given by the
saturation of , where is the canonical sheaf of . We define
the Kodaira dimension of the orbifold base by that of and call
the fibration to be of general type if this dimension is the maximal \dime Y.
We call special if it does not have a general type fibration with positive
dimensional base and call special if its general fibers are. We note that
Iitaka and rationally connected fibrations are special. Our main theorem is
that any compact complex has a special fibration of general type which
dominates any fibration of general type and factors through any special
fibration of general type from in the birational category, thus unique in
this category. Also, the fibration has positive dimensional fibers if is
not of general type thus resolving a problem in Mori's program for varieties
with negative Kodaira dimension. Our main theorem is stated in the full
orbifold context of log pairs as in Mori's program via which we give an
application to the Albanese map of projective manifolds with nef anticanonical
bundle a part of which was derived using positive charateristic techniques by
Qi Zhang.Comment: Some additional theorems and remarks added and corrections mad
Maser mechanism of optical pulsations from anomalous X-ray pulsar 4U0142+61
A maser curvature emission mechanism in the presence of curvature drift is
used to explain the optical pulsations from anomalous X-ray pulsars. For the
source of AXP0142+61,the optical pulsation occurs at the radial distance
cm to the neutron star. The corresponding
curvature maser frequency is about Hz. The
result is consistent with the observation of the optical pulsations from the
anomalous X-ray pulsar 4U0142+61.Comment: 18pages,LaTeX2e, accetpetd for publication in MNRA
Algebraic Surfaces Holomorphically Dominable by C2
An n-dimensional complex manifold M is said to be (holomorphically) dominable
by \CC^n if there is a map F:\CC^n \ra M which is holomorphic such that the
Jacobian determinant is not identically zero. Such a map F is called
a dominating map. In this paper, we attempt to classify algebraic surfaces X
which are dominable by \CC^2 using a combination of techniques from algebraic
topology, complex geometry and analysis. One of the key tools in the study of
algebraic surfaces is the notion of Kodaira dimension (defined in section 2).
By Kodaira's pioneering work and its extensions, an algebraic surface which is
dominable by \CC^2 must have Kodaira dimension less than two. Using the
Kodaira dimension and the fundamental group of X, we succeed in classifying
algebraic surfaces which are dominable by \CC^2 except for certain cases in
which X is an algebraic surface of Kodaira dimension zero and the case when X
is rational without any logarithmic 1-form. More specifically, in the case when
X is compact (namely projective), we need to exclude only the case when X is
birationally equivalent to a K3 surface (a simply connected compact complex
surface which admits a globally non-vanishing holomorphic 2-form) that is
neither elliptic nor Kummer (see sections 3 and 4 for the definition of these
types of surfaces).Comment: 39 page
Positivity criteria for log canonical divisors and hyperbolicity
Let X be a complex projective variety and D a reduced divisor on X. Under a
natural minimal condition on the singularities of the pair (X, D), which
includes the case of smooth X with simple normal crossing D, we ask for
geometric criteria guaranteeing various positivity conditions for the
log-canonical divisor K_X+D. By adjunction and running the log minimal model
program, natural to our setting, we obtain a geometric criterion for K_X+D to
be numerically effective as well as a geometric version of the cone theorem,
generalizing to the context of log pairs these results of Mori. A criterion for
K_X+D to be pseudo-effective with mild hypothesis on D follows. We also obtain,
assuming the abundance conjecture and the existence of rational curves on
Calabi-Yau manifolds, an optimal geometric sharpening of the Nakai-Moishezon
criterion for the ampleness of a divisor of the form K_X+D, a criterion
verified under a canonical hyperbolicity assumption on (X,D). Without these
conjectures, we verify this ampleness criterion with assumptions on the number
of ample and non ample components of D.Comment: Journal f\"ur die reine und angewandte Mathematik (to appear); final
version; this arXiv version contains the proof of Remark 4.9 (2-dimensional
case for dlt pairs) as Appendi
On the nature of the flares from three candidate tidal disruption events
The X-ray flares of NGC 5905, RX J1242.6-1119A, and RX J1624.9+7554 observed
by Chandra in 2001 and 2002 have been suggested as the candidate tidal
disruption events. The distinct features observed from these events may be used
to determine the type of a star tidally disrupted by a massive black hole. We
investigate these three events, focusing on the differences for the tidal
disruption of a giant star and a main sequence, resulted from their different
relation between the mass and the radius. We argue that their X-ray flare
properties could be modeled by the partial stripping of the outer layers of a
solar type star. The tidal disruption of a giant star is excluded completely.
This result may be useful for understanding the growth of a supermassive black
hole by capturing stars, versus the growth mode through continuous mass
accretion.Comment: 3 pages, Conference proceeding to appear in "The Central Engine of
Active Galactic Nuclei", ed. L. C. Ho and J.-M. Wang (San Francisco: ASP
Regularity criterion and classification for algebras of Jordan type
We show that Artin-Schelter regularity of a -graded algebra can
be examined by its associated -graded algebra. We prove that
there is exactly one class of four-dimensional Artin-Schelter regular algebras
with two generators of degree one in the Jordan case. This class is strongly
noetherian, Auslander regular, and Cohen-Macaulay. Their automorphisms and
point modules are described.Comment: 24 page
The structure of connected (graded) Hopf algebras
In this paper, we establish a structure theorem for connected graded Hopf
algebras over a field of characteristic by claiming the existence of a
family of homogeneous generators and a total order on the index set that
satisfy some desirable conditions. The approach to the structure theorem is
constructive, based on the combinatorial properties of Lyndon words and the
standard bracketing on words. As a surprising consequence of the structure
theorem, we show that connected graded Hopf algebras of finite Gelfand-Kirillov
dimension over a field of characteristic are all iterated Hopf Ore
extensions of the base field. In addition, some keystone facts of connected
Hopf algebras over a field of characteristic are observed as corollaries of
the structure theorem, without the assumptions of having finite
Gelfand-Kirillov dimension (or affineness) on Hopf algebras or of that the base
field is algebraically closed.Comment: 25 pages, add more details on some proof
Nonrelativistic phase in gamma-ray burst afterglows
The discovery of multiband afterglows definitely shows that most -ray
bursts are of cosmological origin. -ray bursts are found to be one of
the most violent explosive phenomena in the Universe, in which astonishing
ultra-relativistic motions are involved. In this article, the multiband
observational characteristics of -ray bursts and their afterglows are
briefly reviewed. The standard model of -ray bursts, i.e. the fireball
model, is described. Emphasis is then put on the importance of the
nonrelativistic phase of afterglows. The concept of deep Newtonian phase is
elaborated. A generic dynamical model that is applicable in both the
relativistic and nonrelativistic phases is introduced. Based on these
elaborations, the overall afterglow behaviors, from the very early stages to
the very late stages, can be conveniently calculated.Comment: A review paper accepted for publication in a Chinese journal of:
Progress in Natural Science. 6 figures, 21 page
Nakayama automorphisms of twisted tensor products
In this paper, we study homological properties of twisted tensor products of
connected graded algebras. We focus on the Ext-algebras of twisted tensor
products with a certain form of twisting maps firstly. We show those
Ext-algebras are also twisted tensor products, and depict the twisting maps for
such Ext-algebras in-depth. With those preparations, we describe Nakayama
automorphisms of twisted tensor products of noetherian Artin-Schelter regular
algebras
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