On the canonical divisor of smooth toroidal compactifications

In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three. Moreover, if $n\geq 3$ we show that the numerical dimension of the canonical divisor of a smooth $n$-dimensional compactification is always bigger or equal to $n-1$. We also show that up to a finite \'etale cover all such compactifications have ample canonical class, therefore refining a classical theorem of Mumford and Tai. Finally, we improve in all dimensions $n\geq 3$ the cusp count for finite volume complex hyperbolic manifolds given in [DD15a].Comment: Title shortened to match published versio

Gamma-Ray Astronomy around 100 TeV with a large Muon Detector operated at Very High Altitude

Measurements at 100 TeV and above are an important goal for the next generation of high energy gamma-ray astronomy experiments to solve the still open problem of the origin of galactic cosmic rays. The most natural experimental solution to detect very low radiation fluxes is provided by the Extensive Air Shower (EAS) arrays. They benefit from a close to 90% duty cycle and a very large field of view (about 2 sr), but the sensitivity is limited by their angular resolution and their poor cosmic ray background discrimination. Above 10 TeV the standard technique for rejecting the hadronic background consists in looking for "muon-poor" showers. In this paper we discuss the capability of a large muon detector (A=2500 m2) operated with an EAS array at very high altitude (>4000 m a.s.l.) to detect gamma-ray fluxes around 100 TeV. Simulation-based estimates of energy ranges and sensitivities are presented.Comment: 4 pages, proceedings of the 30th ICRC, Merida, Mexico, 200

A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10) contributions to the SU(3) plaquette

We compute the perturbative expansion of the Lattice SU(3) plaquette to beta^(-10) order. The result is found to be consistent both with the expected renormalon behaviour and with finite size effects on top of that.Comment: 15 pages, 5 colour eps figures. Axes labels added in the figures. A comment added in the appendi

Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable

The n_f=2 residual mass in lattice HQET to alpha^3 order

We compute the so called residual mass in Lattice Heavy Quark Effective Theory to alpha^3 order in the n_f=2 (unquenched) case. The control of this additive mass renormalization is crucial for the determination of the heavy quark mass from lattice simulations. We discuss the impact on an unquenched determination of the b-quark mass.Comment: Lattice2004(heavy), 3 pages, 1 figur

Unquenched Numerical Stochastic Perturbation Theory

The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice SU(3), we report on the performance of the current implementation of the algorithm and the status of first computations undertaken.Comment: 3 pages, 3 figures, Lattice2002(algor

Effects of large field cutoffs in scalar and gauge models

We discuss the notion of a large field cutoff for lattice gauge models with compact groups. We propose and compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and ``small-field'' configurations. We show that the correlations between volume average of field size indicators and the behavior of the tail of the distribution are very different in the gauge and scalar cases. We show that the effect of discarding the large field configurations on the plaquette average is very different above, below and near beta=5.6 for a pure SU(3) LGT.Comment: Lattice2004(theory