8,953 research outputs found
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
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