ar X iv : 0 71 1 . 27 58 v 1 [ m at h . A G ] 1 7 N ov 2 00 7 Rational curves of degree 11 on a general quintic threefold ∗

ar X iv : m at h / 02 07 25 7 v 1 [ m at h . A G ] 2 7 Ju l 2 00 2 RATIONAL CURVES ON HYPERSURFACES OF LOW DEGREE , II

This is a continuation of [7] in which we proved irreducibility of spaces of rational curves on a general hypersurface X d ⊂ P n of degree d < n+1 2. In this paper, we prove that if d 2 + d + 2 ≤ n and if d ≥ 3, then the spaces of rational curves are themselves rationally connected.

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

ar X iv : h ep - p h / 00 11 11 7 v 1 8 N ov 2 00 0 1 ( Mis ) Understanding the Atmospheric Neutrino Anomaly

ar X iv : m at h / 04 10 61 1 v 2 [ m at h . A G ] 1 1 N ov 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : 0 71 1 . 26 95 v 1 [ m at h . SP ] 1 6 N ov 2 00 7 REGULARITY AND THE CESÀRO – NEVAI CLASS

We consider OPRL and OPUC with measures regular in the sense of Ullman–Stahl–Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [−2, 2] implies lim N →∞ N −1 [ N n=1 (a n −1) 2 +b 2 n ] = 0.