A new geometric approach to problems in birational geometry

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties. A fundamental question is the following: given two mildly singular projective varieties with some of the first variety's pseudonormed spaces being isometric to the corresponding ones of the second variety's, can one construct a birational map between them which induces these isometries? In this work a positive answer to this question is given for varieties of general type. This can be thought of as a theorem of Torelli type for birational equivalence.Comment: 13 pages, to appear in PNA

On Kernel Formulas and Dispersionless Hirota Equations

We rederive dispersionless Hirota equations of the dispersionless Toda hierarchy from the method of kernel formula provided by Carroll and Kodama. We then apply the method to derive dispersionless Hirota equations of the extended dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify associativity equations (WDVV equations) in the EdBKP hierarchy from dispersionless Hirota equations and give a realization of associative algebra with structure constants expressed in terms of residue formula.Comment: 30 pages, minor corrections, references adde

Decay Constants of Pseudoscalar DD-mesons in Lattice QCD with Domain-Wall Fermion

We present the first study of the masses and decay constants of the pseudoscalar $D$ mesons in two flavors lattice QCD with domain-wall fermion. The gauge ensembles are generated on the $24^3 \times 48$ lattice with the extent $N_s = 16$ in the fifth dimension, and the plaquette gauge action at $\beta = 6.10$, for three sea-quark masses with corresponding pion masses in the range $260-475$ MeV. We compute the point-to-point quark propagators, and measure the time-correlation functions of the pseudoscalar and vector mesons. The inverse lattice spacing is determined by the Wilson flow, while the strange and the charm quark masses by the masses of the vector mesons $\phi(1020)$ and $J/\psi(3097)$ respectively. Using heavy meson chiral perturbation theory (HMChPT) to extrapolate to the physical pion mass, we obtain $f_D = 202.3(2.2)(2.6)$ MeV and $f_{D_s} = 258.7(1.1)(2.9)$ MeV.Comment: 15 pages, 3 figures. v2: the statistics of ensemble (A) with m_sea = 0.005 has been increased, more details on the systematic error, to appear in Phys. Lett.

Evolutionary dynamics on any population structure

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class which suggests there is no efficient algorithm. Whether there exists a simple solution for weak selection was unanswered. Here we provide, surprisingly, a general formula for weak selection that applies to any graph or social network. Our method uses coalescent theory and relies on calculating the meeting times of random walks. We can now evaluate large numbers of diverse and heterogeneous population structures for their propensity to favor cooperation. We can also study how small changes in population structure---graph surgery---affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.Comment: 68 pages, 10 figure

Magneto-Infrared Spectroscopic Study of Ultrathin Bi2_{2}Te3_{3} Single Crystals

Ultrathin Bi$_{2}$Te$_{3}$ single crystals laid on Scotch tape are investigated by Fourier transform infrared spectroscopy at $4$K and in a magnetic field up to $35$T. The magneto-transmittance spectra of the Bi$_{2}$% Te$_{3}$/tape composite are analyzed as a two-layer system and the optical conductivity of Bi$_{2}$Te$_{3}$ at different magnetic fields are extracted. We find that magnetic field modifies the optical conductivity in the following ways: (1) Field-induced transfer of the optical weight from the lower frequency regime ($<250$cm$^{-1}$) to the higher frequency regime ($$cm$^{-1}$) due to the redistribution of charge carriers across the Fermi surface. (2) Evolving of a Fano-resonance-like spectral feature from an anti-resonance to a resonance with increasing magnetic field. Such behavior can be attributed to the electron-phonon interactions between the $$ optical phonon mode and the continuum of electronic transitions. (3) Cyclotron resonance resulting from the inter-valence band Landau level transitions, which can be described by the electrodynamics of massive Dirac holes

Topological susceptibility in finite temperature QCD with physical (u/d,s,c)(u/d, s, c) domain-wall quarks

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1$ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150$ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $\chi_t(a,T)$ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $\chi_t(a,T)$ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516$ MeV, we extract the topological susceptibility $\chi_t(T)$ in the continuum limit. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.Comment: 36 pages, 5 figure