51 research outputs found
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Prediction of Anisotropic Single-Dirac-Cones in BiSb Thin Films
The electronic band structures of BiSb thin films can be
varied as a function of temperature, pressure, stoichiometry, film thickness
and growth orientation. We here show how different anisotropic
single-Dirac-cones can be constructed in a BiSb thin film for
different applications or research purposes. For predicting anisotropic
single-Dirac-cones, we have developed an iterative-two-dimensional-two-band
model to get a consistent inverse-effective-mass-tensor and band-gap, which can
be used in a general two-dimensional system that has a non-parabolic dispersion
relation as in a BiSb thin film system
Special Libraries, April 1933
Volume 24, Issue 3https://scholarworks.sjsu.edu/sla_sl_1933/1002/thumbnail.jp
Curves with infinite K-rational geometric fundamental group
this paper we shall use either quartic coverings of the projective line or quadratic coverings of elliptic curves with enough ramification points (instead of quadratic coverings of the projective line as in the class field tower constructions) to find for every genus g 3 curves with infinite geometric fundamental group defined over Q(i) or over F q (i) (where i is a forth root of unity) and we find even parametric families of such curves over every ground field containing i (cf. Theorem 5.22)
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