The numerical equivalence relation for height functions and ampleness and nefness criteria for divisors

In this paper, we study properties of Weil height functions associated with numerically trivial divisors. It helps us to define the fractional limit of $h_E$ with respect to $h_D$ on $U$, with $D$ ample: \Flim_D(E,U) := \liminf_{\substack{P \in U h_D(P) \rightarrow \infty}}\dfrac{h_E(P)}{h_D(P)}. The value of \Flim_D(E,U) contains numerical information about a divisor $E$, enough to determine whether $E$ is ample, numerically effective or pseudo-effective

Infrared Supernova Remnants in the Spitzer GLIMPSE Field

We have searched for infrared emission from supernova remnants (SNRs) included in the Spitzer Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) field. At the positions of 100 known SNRs, we made 3.6, 4.5, 5.8, and 8.0 um band images covering the radio continuum emitting area of each remnant. In-depth examinations of four band images based on the radio continuum images of SNRs result in the identification of sixteen infrared SNRs in the GLIMPSE field. Eight SNRs show distinct infrared emission in nearly all the four bands, and the other eight SNRs are visible in more than one band. We present four band images for all identified SNRs, and RGB-color images for the first eight SNRs. These images are the first high resolution (<2") images with comparative resolution of the radio continuum for SNRs detected in the mid-infrared region. The images typically show filamentary emission along the radio enhanced SNR boundaries. Most SNRs are well identified in the 4.5 and 5.8 um bands. We give a brief description of the infrared features of the identified SNRs.Comment: 30 pages including 24 figures, published in JKAS (Journal of the Korean Astronomical Society