Alternating groups and moduli space lifting Invariants

Details Alternating groups and moduli space lifting Invariants Alternating groups and moduli space lifting Invariants

2006-11-20

arxiv.org/abs/math/0611591v4

Israel J. Math. 179 (2010) 57-125

Mathematics

Number Theory

To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in

Scientific paper

10.1007/s11856-010-0073-2

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 .

Affiliated with

Also associated with

No associations

Rating

Alternating groups and moduli space lifting Invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Alternating groups and moduli space lifting Invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Alternating groups and moduli space lifting Invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-120728