Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.Comment: 31 pages; revise

A geometric degree formula for A-discriminants and Euler obstructions of toric varieties

AbstractWe give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and Zelevinsky. Our formulas can be applied also to the case where the A-discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations A. Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given

Was Martian mantle wet? A possible consequence of rapid core formation

Degassing of H2O in the planetary interior possibly plays an important role in the evolution of surface environment as well as geologic activity on the terrestrial planets. Mars may be such a planet that well preserves the materials and the geologic features directly related to early evolution of H2O. H2O content in the interior of proto-Mars during accretion and also core formation were investigated. Geodetic data shows that Mars has a dense core. The existence of iron-rich core on Mars may be also supported by the depletion of siderophile elements in SNC meteorites assuming that these samples came from Mars. Isotope systematics of these meteorites indicate that the core formation occurred very early, probably concurrently with Mars formation. Considering the kinetics of metal segregation from silicate, the melting of silicate is likely to precede the core formation. Once the core formation occurs, substantial amount of gravitational energy is released and thus the planetary interior is heated. This energy may be large enough to keep the silicate material in partially molten state along with the accretional heating. Under such circumstances, the silicate melt probably migrates to the surface. Early crustal formation, therefore, is also likely to be associated with the core formation

Hadronic decays of B→a1(1260)b1(1235)B \to a_1(1260) b_1(1235) in the perturbative QCD approach

We calculate the branching ratios and polarization fractions of the $B \to a_1 b_1$ decays in the perturbative QCD(pQCD) approach at leading order, where $a_1$($b_1$) stands for the axial-vector $a_1(1260)[b_1(1235)]$ state. By combining the phenomenological analyses with the perturbative calculations, we find the following results: (a) the large decay rates around $10^{-5}$ to $10^{-6}$ of the $B \to a_1 b_1$ decays dominated by the longitudinal polarization(except for the $B^+ \to b_1^+ a_1^0$ mode) are predicted and basically consistent with those in the QCD factorization(QCDF) within errors, which are expected to be tested by the Large Hadron Collider and Belle-II experiments. The large $B^0 \to a_1^0 b_1^0$ branching ratio could provide hints to help explore the mechanism of the color-suppressed decays. (b) the rather different QCD behaviors between the $a_1$ and $b_1$ mesons result in the destructive(constructive) contributions in the nonfactorizable spectator diagrams with $a_1(b_1)$ emission. Therefore, an interesting pattern of the branching ratios appears for the color-suppressed $B^0 \to a_1^0 a_1^0, a_1^0 b_1^0,$ and $b_1^0 b_1^0$ modes in the pQCD approach, $Br(B^0 \to b_1^0 b_1^0) > Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$, which is different from $Br(B^0 \to b_1^0 b_1^0) \sim Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$ in the QCDF and would be verified at future experiments. (c) the large naive factorization breaking effects are observed in these $B \to a_1 b_1$ decays. Specifically, the large nonfactorizable spectator(weak annihilation) amplitudes contribute to the $B^0 \to b_1^+ a_1^-(B^+ \to a_1^+ b_1^0\; {\rm and}\; B^+ \to b_1^+ a_1^0)$ mode(s), which demand confirmations via the precise measurements.Comment: 13 pages, 1 figure, 5 tables, revtex fil