The space of arcs of an algebraic variety

The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.Comment: 29 pages; v3 corrects some typos. To appear in the Proceedings of the 2015 Summer Institute on Algebraic Geometr

MONOLITH: a high resolution neutrino oscillation experiment

MONOLITH is a proposed massive magnetized tracking calorimeter at the Gran Sasso laboratory in Italy, optimized for the detection of atmospheric muon neutrinos. The main goal is to test the neutrino oscillation hypothesis through an explicit observation of the full first oscillation swing. The sensitivity range for this measurement comfortably covers the entire Super-Kamiokande allowed region. Other measurements include studies of matter effects, the NC/CC and neutrino/anti-neutrino ratio with atmospheric neutrinos and auxiliary measurements from the CERN to Gran Sasso neutrino beam. Depending on approval, data taking with part of the detector could start in 2005. The MONOLITH detector and its performance are described.Comment: 8 pages, contribution to Les rencontres de Physique de la Vallee d'Aoste, March 200

Limits of log canonical thresholds

Let T_n denote the set of log canonical thresholds of pairs (X,Y), with X a nonsingular variety of dimension n, and Y a nonempty closed subscheme of X. Using non-standard methods, we show that every limit of a decreasing sequence in T_n lies in T_{n-1}, proving in this setting a conjecture of Koll\'{a}r. We also show that T_n is a closed subset in the set of real numbers; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check Shokurov's ACC Conjecture for all T_n, it is enough to show that 1 is not a point of accumulation from below of any T_n. In a different direction, we interpret the ACC Conjecture as a semi-continuity property for log canonical thresholds of formal power series.Comment: 26 pages; revised version, to appear in Ann. Sci. Ecole Norm. Su