Lang maps and Harris’s conjecture

We show that any variety in characteristic 0 possesses a universal dominant rational map, which we callthe Lang map, to a variety of general type. We discuss a conjecture of J. Harris regarding the relation between rational points and Lang maps. Partially supported by NSF grant DMS-9503276.     

Microheterogeneity of benzene solutions of cyclohexane, 1,4-dioxane,and morpholine

Data obtained in molecular light scattering, adiabatic compressibility, and molar volume studies of benzene solutions of cyclohexane, 1,4-dioxane, and morpholine were used to suggest a model of the structure of these solutions and show that microheterogeneity of solutions was caused by the presence of agglomerates comprising benzene molecules in the benzene-cyclohexane system and conglomerates including heteromolecular interactions in the other systems.     

Analysis of experimental data on the key thermonuclear reactions going within the low energy range

A comparative analysis of experimental data on hydrogen and helium isotope interaction with deuterons and tritons at low energy is performed. If the energy of an incident particle falls to several keV, the astrophysical factor S(E) rises sharply, indicating that there is an electron screening effect for such interaction. The values of electron screening potentials and enhancement factors are given for key thermonuclear reactions. It is important to allow for the electron screening effect in calculations performed during astrophysical research and in designing different thermonuclear facilities.     

Relationship between spontaneous generation of voltage and structural features in a single crystal of Pr0.6Ca0.4MnO3

Spontaneous generation of electrical voltage U was found for the perovskite-like single crystal of Pr_0.6Ca_0.4MnO₃, wherein the charge and orbital orderings occur at T _CO = 240 K and the antiferromagnetic one occurs at the Neel point T _N = 174 K. With decreasing the temperature, the U value increases first slowly (in the temperature range of 300 K-T _CO) and then more rapidly (T _CO-T _N). Starting from T _N, U increases exponentially and, at 85 K, reaches the value of 115 mV (in the ab plane) and 6.5 mV (along the c axis). The magnetic field has a different effect on the U value in different temperature ranges: in the temperature range of 85–130 K, it decreases U and, in the range of 130–240 K, increases U. The spontaneous voltage is thought to be caused by the existence of ferromagnetic and charge-orbital-ordered clusters of different topology in the sample. The latter clusters have own features and their structure are described by the non-centrosymmetric space group P2₁ nm.     

Relation between giant volume magnetostriction and colossal magnetoresistance near the Curie temperature of Sm0.55Sr0.45MnO3

The magnetic, transport, and elastic properties of Sm_0.55Sr_0.45MnO₃ have been established to be interrelated. At the Curie point, one observes a large volume compression ΔV/V≈0.1%, a sharp minimum in the temperature dependence of negative volume magnetostriction ω(T), and a maximum in the temperature dependence of the electrical resistivity. Giant negative volume magnetostriction ω=?5×10^?4 has been found in a magnetic field H=0.9 T, which is accompanied by a colossal negative magnetoresistance of 44% in the same field. The results obtained are discussed in terms of a model of electronic phase separation.     

Peculiarities of magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Eu<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript>

Magnetic, elastic, magnetoelastic, transport, and magnetotransport properties of the Eu_0.55Sr_0.45MnO₃ ceramics have been studied. A break was detected in the temperature dependence of electrical resistivity ρ(T) near the temperature of the magnetic phase transformation (41 K), with the material remaining an insulator down to the lowest measurement temperature reached (ρ=10⁶ Ω cm at 4.2 K). In the interval 4.2≤T≤50 K, the isotherms of the magnetization, volume magnetostriction, and ρ were observed to undergo jumps at the critical field H_C1, which decreases with increasing T. For 50≤T≤120 K, the jumps in the above curves persist, but the pattern of the curves changes and H_C1 grows with increasing T. The magnetoresistance Δρ/ρ = (ρ _H ?ρ_H=0)/ρ _H is positive for H<H_C1 and passes through a maximum at 41 K, where Δρ/ρ = 6%. For H>H_C1, the magnetoresistance is negative, passes through a minimum near 41 K, and reaches a colossal value of 3×10⁵ % at H=45 kOe. The volume magnetostriction is negative and attains a giant value of 4.5×10^?4atH=45 kOe. The observed properties are assigned to the existence of three phases in Eu_0.55Sr_0.45MnO₃, namely, a ferromagnetic (FM) phase, in which carriers are concentrated because of the gain in s-d exchange energy, and two antiferromagnetic (AFM) phases of the A and CE types. Their fractional volumes at low temperatures were estimated to be as follows: ～3% of the sample volume is occupied by the FM phase; ～67%, by the CE-type AFM phase; and ～30%, by the A-type AFM phase.     

Moduli of twisted spin curves

In this note we give a new, natural construction of a compactification of the stack of smooth -spin curves, which we call the stack of stable twisted -spin curves. This stack is identified with a special case of a stack of twisted stable maps of Abramovich and Vistoli. Realizations in terms of admissible -spaces and -line bundles are given as well. The infinitesimal structure of this stack is described in a relatively straightforward manner, similar to that of usual stable curves.

We construct representable morphisms from the stacks of stable twisted -spin curves to the stacks of stable -spin curves and show that they are isomorphisms. Many delicate features of -spin curves, including torsion free sheaves with power maps, arise as simple by-products of twisted spin curves. Various constructions, such as the -operator of Seeley and Singer and Witten's cohomology class go through without complications in the setting of twisted spin curves.

     

Torification and factorization of birational maps

Building on work of the fourth author and Morelli's work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.

     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.