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⁡(fijˉ)=1\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

A Finite Rank Bundle over JJ-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

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

The Exponential Decay of Gluing Maps for JJ-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