Syzygies, multigraded regularity and toric varieties

Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B_1, ..., B_k on X and integers m_1, ..., m_k, consider the line bundle L := B_1^m_1 \otimes ... \otimes B_k^m_k. We give conditions on the m_i which guarantee that the ideal of X in P(H^0(X,L)) is generated by quadrics and the first p syzygies are linear. This yields new results on the syzygies of toric varieties and the normality of polytopes.Comment: improved exposition and corrected typo

Muon spin rotation and relaxation in the superconducting ferromagnet UCoGe

We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $\mu^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $\mu$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.Comment: 4 pages, 3 figures, accepted for publication in PR

Euler characteristic of coherent sheaves on simplicial torics via the Stanley-Reisner ring

We combine work of Cox on the total coordinate ring of a toric variety and results of Eisenbud-Mustata-Stillman and Mustata on cohomology of toric and monomial ideals to obtain a formula for computing the Euler characteristic of a Weil divisor D on a complete simplicial toric variety in terms of graded pieces of the Cox ring and Stanley-Reisner ring. The main point is to use Alexander duality to pass from the toric irrelevant ideal, which appears in the computation of the Euler characteristic of D, to the Stanley-Reisner ideal of the fan, which is used in defining the Chow ring. The formula also follows from work of Maclagan-Smith.Comment: 9 pages 1 figur

Penetration depth, multiband superconductivity, and absence of muon-induced perturbation in superconducting PrOs4_{4}Sb12_{12}

Transverse-field muon spin rotation ($\mu$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $\lambda(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $\lambda(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the perturbing effect of the muon charge on the neighboring Pr$^{3+}$ crystalline electric field is negligibly small, and therefore is unlikely to cause the difference between the $\mu$SR and rf results.Comment: 10 pages, 7 figure

Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)6_6][Mn(SS)-pnH(H2_2O)](H2_2O) Probed by Muon Spin Rotation and Relaxation

Local magnetic fields in a molecule-based optically chiral magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) (GN-S) and its enantiomer (GN-R) are studied by means of muon spin rotation and relaxation (muSR). Detailed analysis of muon precession signals under zero field observed below T_c supports the average magnetic structure suggested by neutron powder diffraction. Moreover, comparison of muSR spectra between GN-S and GN-R suggests that they are a pair of complete optical isomers in terms of both crystallographic and magnetic structure. Possibility of magnetic chirality in such a pair is discussed.Comment: 5 pages, 5 figures, submitted to J. Phys. Soc. Jp

Hidden magnetic order in CuNCN

We report a comprehensive experimental and theoretical study of the quasi-one-dimensional quantum magnet CuNCN. Based on magnetization measurements above room temperature as well as muon spin rotation and electron spin resonance measurements, we unequivocally establish the localized Cu+2-based magnetism and the magnetic transition around 70 K, both controversially discussed in the previous literature. Thermodynamic data conform to the uniform-spin-chain model with a nearest-neighbor intrachain coupling of about 2300 K, in remarkable agreement with the microscopic magnetic model based on density functional theory band-structure calculations. Using exact diagonalization and the coupled-cluster method, we derive a collinear antiferromagnetic order with a strongly reduced ordered moment of about 0.4 mu_B, indicating strong quantum fluctuations inherent to this quasi-one-dimensional spin system. We re-analyze the available neutron-scattering data, and conclude that they are not sufficient to resolve or disprove the magnetic order in CuNCN. By contrast, spectroscopic techniques indeed show signatures of long-range magnetic order below 70 K, yet with a rather broad distribution of internal field probed by implanted muons. We contemplate the possible structural origin of this effect and emphasize peculiar features of the microstructure studied with synchrotron powder x-ray diffraction.Comment: 17 pages, 17 figures, 1 tabl

Delocalization of slowly damped eigenmodes on Anosov manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a "strip" of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two reference

Evidence for an antiferromagnetic component in the magnetic structure of ZrZn2

Zero-field muon spin rotation experiments provide evidence for an antiferromagnetic component in the magnetic structure of the intermetallics ZrZn2.Comment: 5 pages, 2 figure

Spin dynamics in copper metaborate CuB2O4CuB_2 O_4 studied by muon spin relaxation

Copper metaborate CuB$_2$O$_{4}$ was studied by muon spin relaxation measurements in order to clarify its static and dynamic magnetic properties. The time spectra of muon spin depolarization suggest that the local fields at the muon site contain both static and fluctuating components in all ordered phases down to 0.3 K. In the weak ferromagnetic phase (20 K~$>T>$~9.3 K), the static component is dominant. On the other hand, upon cooling the fluctuating component becomes dominant in the incommensurate helix phase (9.3K > T > 1.4K). The dynamical fluctuations of the local fields persist down to 0.3K, where a new incommensurate phase (T < 1.4K) is expected to appear. This result suggests that spins fluctuate even at T \to 0. We propose two possible origins of the remnant dynamical spin fluctuations: frustration of the exchange interactions and the dynamic behavior of the soliton lattice