Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of a purely arithmetic property of variety and its metrical property, and partially confirm it.Comment: 47 pages. Final version, to appear in Kyoto Journal of Mathematic

Tropical Geometric Compactification of Moduli, II - AgA_g case and holomorphic limits -

We compactify the classical moduli variety $A_g$ of principally polarized abelian varieties of complex dimension $g$ by attaching the moduli of flat tori of real dimensions at most $g$ in an explicit manner. Equivalently, we explicitly determine the Gromov-Hausdorff limits of principally polarized abelian varieties. This work is analogous to the first of our series (available at arXiv:1406.7772v2), which compactified the moduli of curves by attaching the moduli of metrized graphs. Then, we also explicitly specify the Gromov-Hausdorff limits along holomorphic family of abelian varieties and show that they form special non-trivial subsets of the whole boundary. We also do it for algebraic curves case and observe a crucial difference with the case of abelian varieties.Comment: Extended revision of the LATTER half (Abelian varieties case, $A_g$ case) of the original version 1 of arXiv:1406.7772. Many contents added. Submitte

Simulation of ZZ boson pTp_{T} spectrum at Tevatron by leading-order event generators

We show that the transverse momentum ($p_{T}$) spectrum of $Z$ boson production measured at Fermilab Tevatron can be well reproduced by leading-order event generators if $Z$ + 1 jet processes are included with a proper solution for the double-count problem and if the parton shower (PS) branch kinematics are defined appropriately. The choice of the PS evolution variable does not definitely determine the low-$p_{T}$ behavior. Our new event generator employing the limited leading-log (LLL) subtraction and a built-in leading-log PS reproduces the spectrum very well, not only in large $p_{T}$ regions but also at low $p_{T}$ down to $p_{T}$ = 0.Comment: 13 pages, 4 figures: explanations were added to clarify the discussions. Minor changes for publicatio

Spin Connections and Classification of Inequivalent Quantizations

We discuss an extension of the quantization method based on the induced representation of the canonical group.Comment: 4 pages, no figure

On the moduli of Kahler-Einstein Fano manifolds

We prove that Kahler-Einstein Fano manifolds with finite automorphism groups form Hausdorff moduli algebraic space with only quotient singularities. We also discuss the limits as Q-Fano varieties which should be put on the boundary of its canonical compactification.Comment: 15 pages. Final version appeared in Proceeding of Kinosaki algebraic geometry symposium 2013. (I am sorry for late upload

Tropical Geometric Compactification of Moduli, I - MgM_g case -

We compactify the classical moduli variety of compact Riemann surfaces by attaching moduli of (metrized) graphs as boundary. The compactifications do not admit the structure of varieties and patch together to form a big connected moduli space in which $\sqcup_{g} M_{g}$ is open dense. The metrized graphs, which are often studied as "tropical curves", are obtained as Gromov-Hausdorff collapse by fixing diameters of the hyperbolic metrics of the Riemann surfaces. This phenomenon can be also seen as an archemidean analogue of the tropicalization of Berkovich analytification of $M_{g}$ (cf., [ACP]).Comment: v2: Revision of the FORMER half (curve, $M_g$ case) of version 1. v3: revised exposition of v2. Re-submitte

Precise simulation of the initial-state QCD activity associated with ZZ-boson production in hadron collisions

The $\phi_{\eta}^{*}$ distribution of the $Z/\gamma^{*} \rightarrow \ell^{+}\ell^{-}$ production in hadron collisions is simulated using a leading-order event generator, GR@PPA. The initial-state parton shower, which simulates the multiple QCD-radiation effects in the initial state, plays the dominant role in this simulation. The simulation in the default setting agrees with the high-statistics measurement by ATLAS at LHC with the precision at the level of 5%. The observed systematic deviation, which can be attributed to the effects of ignored higher-order contributions, can be reduced by adjusting the arbitrary energy scales in the simulation. The agreement at the level of 1% can be achieved over a very wide range without introducing any modification in the implemented naive leading-logarithmic parton shower.Comment: 9 pages, 4 figure

A generalization of Ross-Thomas' slope theory

We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki invariants implies K-stability (resp. K-semistability). We show its applicability by proving K-(semi)stability of certain polarized varieties with semi-log-canonical singularities, generalizing some results by Ross-Thomas.Comment: 15 pages. v2-4:minor changes, v5:re-edited (the latter half moved to arXiv:0807.1716 v5

A simple method to simulate W/Z + jet production at hadron collisions with PS-ME matching

We propose a simple method to simulate $W/Z$ + jet productions at hadron collisions. The simulation can be done by using existing tools with some modifications allowed to users. $W/Z$ + 1 jet events are generated using an ME-based event generator at the tree level. The divergence at low $p_{T}$ is suppressed by using the Sudakov form factor. PS is added with an appropriate consideration for PS-ME matching. The simulation for the $W$ + 1 jet production shows a smooth matching with the $W$ + 0 jet simulation at low $p_{T}$s. The $Z$ + 1 jet simulation in the Tevatron Run I condition well reproduces the experimental measurement on the $p_{T}$ spectrum of $Z$.Comment: 13 pages, 8 figures; corrections in the introduction and related references, added the alpha_s definition in section

Comment on qq-deformation in Second Quantization Procedure

When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under the coaction of the quantum group. In the 1+1 dimensional quantum field theories we deform the algebra of the basis vectors and study the $q$-deformation in the second quantization procedure.Comment: NDA-FP-9/92, 9pp, phyzzx.te