Particle theory

Abstract:

In this paper we describe the first results of a compact imaging air-Cherenkov telescope, IceAct, operating in coincidence with the IceCube Neutrino Observatory (IceCube) at the geographic South Pole. An array of IceAct telescopes (referred to as the IceAct project) is under consideration as part of the IceCube-Gen2 extension to IceCube. Surface detectors in general will be a powerful tool in IceCube-Gen2 for distinguishing astrophysical neutrinos from the dominant backgrounds of cosmic-ray induced atmospheric muons and neutrinos: the IceTop array is already in place as part of IceCube, but has a high energy threshold. Although the duty cycle will be lower for the IceAct telescopes than the present IceTop tanks, the IceAct telescopes may prove to be more effective at lowering the detection threshold for air showers. Additionally, small imaging air-Cherenkov telescopes in combination with IceTop, the deep IceCube detector or other future detector systems might improve measurements of the composition of the cosmic ray energy spectrum. In this paper we present measurements of a first 7-pixel imaging air Cherenkov telescope demonstrator, proving the capability of this technology to measure air showers at the South Pole in coincidence with IceTop and the deep IceCube detector.

Abstract:

We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any line bundle cohomology in terms of an index. These formulae follow from general theorems we prove for a wider class of surfaces. In particular, we construct a map that takes any effective line bundle to a nef line bundle while preserving the zeroth cohomology dimension. For complex surfaces, these results explain the appearance of piecewise polynomial equations for cohomology and they are a first step towards understanding similar formulae recently obtained for Calabi-Yau three-folds.