55,820 research outputs found

### The Topological Structure of Nieh-Yan Form and Chiral Anomaly in Spaces with Torsion

The topological structure of the Nieh-Yan form in 4-dimensional manifold is
given by making use of the decomposition of spin connection. The case of the
generalized Nieh-Yan form on $2^d$-dimensional manifold is discussed with an
example of 8-dimensional case studied in detail. The chiral anomaly with
nonvanishing torsion is studied also. The further contributions from torsional
part to chiral anomaly are found coming from the zeroes of some fields under
pure gauge condition.Comment: Revtex, 12 page

### On the invariants of base changes of pencils of curves, II

In this part of the series, we shall investigate Deligne-Mumford semistable
reductions from the point of view of numerical invariants. As an application,
we obtain two numerical criterions for a base change to be stabilizing, and for
a fibration to be isotrivial. We also obtain a canonical class inequality for
any fibration. Some other applications are presented. Most of the results of
this paper have arithmetical analogues. This paper will appear in Math. Z.Comment: 21 pages, AmSTe

### A Liouville Theorem on the PDE $\det(f_{i\bar j})=1$

Let $f$ be a smooth plurisubharmonic function which solves \det(f_{i\bar
j})=1\;\;\;\;\;\;\mbox{in }\Omega\subset \mathbb C^n. Suppose that the metric
$\omega_{f}=\sqrt{-1}f_{i\bar j}dz_{i}\wedge d\bar z_{j}$ is complete and $f$
satisfies the growth condition $C^{-1}(1+|z|^2)\leq f\leq C(1+
|z|^2),\;\;\;\; as\;\;\; |z|\to \infty.$ for some $C>0,$ then $f$ is
quadratic

### Contact Invariants, Open String Invariants and Weinstein Conjecture

We propose a theory of contact invariants and open string invariants,
assuming that the almost complex $J$ is either non-degenerate or of Bott-type.
We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$
on periodic orbits.Comment: 13pages. arXiv admin note: substantial text overlap with
arXiv:1501.0109

### A Finite Rank Bundle over $J$-Holomorphic map Moduli Spaces

We study a finite rank bundle $\mathbf{F}$ over a neighborhood of
$J$-Holomorphic map Moduli Spaces, prove the exponential decay of the
derivative of the gluing maps for $\mathbf{F}$ with respect to the gluing
parameter.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1710.10581,
arXiv:1506.0633

### Height inequality of algebraic points on curves over functional fields

The purpose of this paper is to give a linear and effective height inequality
for algebraic points on curves over functional fields. Our height inequality
can be viewed as the logarithmic canonical class inequality of a punctured
curve over a functional field (a fibered surface minus a section).Comment: 14 pages, AmSTeX 2.1 This paper will appear in J. reine angew. Mat

### The Exponential Decay of Gluing Maps for $J$-Holomorphic map Moduli Spaces

We prove the exponential decay of the derivative of the gluing maps with
respect to the gluing parameter.Comment: v3 title changed, 36pages. v2 26pages, minor revision. v1 25pages.
Welcome comment

### A Pati-Salam model from square root Lorentz manifold

There is a $U(4^{\prime})\times U(4)$-bundle on four-dimensional square root
Lorentz manifold. Then a Pati-Salam model in curved space-time and a gravity
theory can be constructed on square root Lorentz manifold. The Sheaf
quantization method is shown and the transition amplitude in path integral
quantization is given.Comment: 7 pages, 4 figure

### The minimal number of singular fibers of a semistable curves over P^1

In this paper, we shall prove Beauville's conjecture: if $f:S \to P^1$ is a
non-trivial semistable fibration of genus g>1, then $f$ admits at least 5
singular fibers. We have also constructed an example of genus 2 with 5 singular
fibers. This paper will appear in the Journal of Algebraic Geometry.Comment: 6 pages, AmSTe

### Virtual Neighborhood Technique for Holomorphic Curve Moduli Spaces

In this paper we use the approach of Ruan and Li-Ruan to construct virtual
neighborhoods and show that the Gromov-Witten invariants can be defined as an
integral over top strata of virtual neighborhood. We prove that the invariants
defined in this way satisfy all the Gromov-Witten axioms of Kontsevich and
Manin.Comment: Any comments are welcome. 44 pages,(47pages,v2

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