Basepoint freeness for nef and big line bundles in positive characteristic

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over M_g, specifically, the semi-ampleness of the relative dualizing sheaf, in positive characteristic. An example is given which shows this and the semi-ampleness criterion fail in characteristic zero. A second application is to Mori's program for minimal models of 3-folds in positive characteristic, namely, to the existence of birational extremal contractions.Comment: 34 pages, published versio

Star formation around active galactic nuclei

Active galactic nuclei (Seyfert nuclei and their relatives) and intense star formation can both deliver substantial amounts of energy to the vicinity of a galactic nucleus. Many luminous nuclei have energetics dominated by one of these mechanisms, but detailed observations show that some have a mixture. Seeing both phenomena at once raises several interesting questions: (1) Is this a general property of some kinds of nuclei? How many AGNs have surround starbursts, and vice versa? (2) As in 1, how many undiscovered AGNs or starbursts are hidden by a more luminous instance of the other? (3) Does one cause the other, and by what means, or do both reflect common influences such as potential well shape or level of gas flow? (4) Can surrounding star formation tell us anything about the central active nuclei, such as lifetimes, kinetic energy output, or mechanical disturbance of the ISM? These are important points in the understanding of activity and star formation in galactic nuclei. Unfortunately, the observational ways of addressing them are as yet not well formulated. Some preliminary studies are reported, aimed at clarifying the issues involved in study of the relationships between stellar and nonstellar excitement in galactic nuclei

The role of shocks in NGC 6240

The case of the infrared-bright system NGC 6240 encapsulates in many ways the major issues in understanding processes in infrared-bright systems in general. Its morphology strongly suggests that this is a merger in progress, with energetic phenomena being triggered as evidenced by strong radio emission and optical emission lines as well as the strong far-infrared output. Evidence has been produced supporting various schemes for producing the energy being radiated by this object. Early work on the optical spectrum suggested a Seyfert 2 classification, but the ionization level and spatial extent of the emission implied a more distributed source of energy. IR line studies found evidence for young supergiants, and for immense amounts of H2 excited by low-velocity shocks, which might contribute to a large enhancement in star-formation rate. Finally, the radio-continuum morphology shows compact sources possibly associated with active nuclei in both remnants of the merger. This is one of the nearest IR-bright galaxies objects at high luminosity (Cz = 7500 km s(exp -1), so that spatially resolved studies can yield further insight into which of these processes are most important - star formation, nuclear activity, or shock excitation. The velocity field, linewidth distribution, and ionization structure of the gas in NGC 6240 was mapped with the Dense-Pak fiber-optic array on the Kitt Peak 4-m telescope. In all, 135 spectra were obtained through an array of 2 inch apertures, with considerable overlap between many of the adjacent apertures produced by offsetting the telescope between the exposures. As the strongest features with lambda less than 1.1 ma, H alpha and the adjacent (NII) lines were observed, along with the neighboring (O I) and (S II) features. Maps of velocity and linewidth were constructed by interpolating measurements from these spectra onto a regular grid, and show irregular patterns with large velocity gradients and, particularly, an extended region of large local (shear?) velocity width