Some results on rational surfaces and Fano varieties

The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle L on X, we give an optimal numerical criterion for L to satisfy property Np. This criterion turns out to be a characterization of property Np if X is anticanonical. We also prove syzygy results for adjunction bundles and a Reider type theorem for higher syzygies. For certain Fano varieties we also prove results on very ampleness and higher syzygies.Comment: 26 pages, AMSTe

Effect of spin-orbit interaction on a magnetic impurity in the vicinity of a surface

We propose a new mechanism for surface-induced magnetic anisotropy to explain the thickness-dependence of the Kondo resistivity of thin films of dilute magnetic alloys. The surface anisotropy energy, generated by spin-orbit coupling on the magnetic impurity itself, is an oscillating function of the distance d from the surface and decays as 1/d^2. Numerical estimates based on simple models suggest that this mechanism, unlike its alternatives, gives rise to an effect of the desired order of magnitude.Comment: 4 pages, 4 figure

Mapping the star formation history of Mrk86: I. Data and models

We have obtained optical (BVR, [OIII]5007 and Halpha), near infrared (JHK) imaging and long-slit optical spectroscopy for the Blue Compact Dwarf galaxy Mrk86 (NGC2537). In this paper, the first of two, we present optical-near- infrared colors and emission-line fluxes for the currently star-forming regions, intemediate aged starburst and underlying stellar population. We also describe the evolutionary synthesis models used in Paper II. The R and Halpha luminosity distributions of the galaxy star-forming regions show maxima at M_R=-9.5 and L_Halpha=10^37.3 erg s^-1. The underlying stellar population shows an exponential surface brigthness profile with central value, mu_E,0=21.5 mag arcsec^-2, and scale, alpha=0.88 kpc, both measured in the R-band image. In the galaxy outer regions, dominated by this component, no significant color gradients are observed. Finally, a set of evolutionary synthesis models have been developed, covering a wide range in metallicity and burst strength.Comment: 21 pages, 14 figures, 2 landscape tables, accepted for publication in Astronomy & Astrophysics Supplement Series, for higher resolution images see ftp://cutrex.fis.ucm.es/pub/OUT/gil/PAPERS/aa00_I.ps.g