4,489 research outputs found
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 - case and holomorphic limits -
We compactify the classical moduli variety of principally polarized
abelian varieties of complex dimension by attaching the moduli of flat tori
of real dimensions at most 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,
case) of the original version 1 of arXiv:1406.7772. Many contents added.
Submitte
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
Simulation of -boson spectrum at LHC and Tevatron using GR@PPA
Predictions from the GR@PPA event generator concerning the
transverse-momentum () spectrum of bosons are compared with recent
measurements at LHC and Tevatron. The simulation results are in reasonable
agreement with the measurements, although marginal discrepancies are observed
in high- regions. The principal agreements imply that the leading-order
simulation with a primitive parton shower based on the leading-logarithmic
approximation still provides a reasonable description of the transverse motion
of the hard-interaction system in hadron collisions, without the need to
introduce noble techniques to incorporate higher-order corrections.Comment: 9 pages, 5 figure
Precise simulation of the initial-state QCD activity associated with -boson production in hadron collisions
The distribution of the 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
Tropical Geometric Compactification of Moduli, I - 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 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
(cf., [ACP]).Comment: v2: Revision of the FORMER half (curve, case) of version 1. v3:
revised exposition of v2. Re-submitte
Simulation of boson spectrum at Tevatron by leading-order event generators
We show that the transverse momentum () spectrum of boson
production measured at Fermilab Tevatron can be well reproduced by
leading-order event generators if + 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- 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
regions but also at low down to = 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
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 + jet productions at hadron
collisions. The simulation can be done by using existing tools with some
modifications allowed to users. + 1 jet events are generated using an
ME-based event generator at the tree level. The divergence at low is
suppressed by using the Sudakov form factor. PS is added with an appropriate
consideration for PS-ME matching. The simulation for the + 1 jet production
shows a smooth matching with the + 0 jet simulation at low s. The
+ 1 jet simulation in the Tevatron Run I condition well reproduces the
experimental measurement on the spectrum of .Comment: 13 pages, 8 figures; corrections in the introduction and related
references, added the alpha_s definition in section
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