The Brill-Noether rank of a tropical curve

We construct a space classifying divisor classes of a fixed degree on all tropical curves of a fixed combinatorial type and show that the function taking a divisor class to its rank is upper semicontinuous. We extend the definition of the Brill-Noether rank of a metric graph to tropical curves and use the upper semicontinuity of the rank function on divisors to show that the Brill-Noether rank varies upper semicontinuously in families of tropical curves. Furthermore, we present a specialization lemma relating the Brill-Noether rank of a tropical curve with the dimension of the Brill-Noether locus of an algerbaic curve.Comment: 17 pages, 4 figures; v2: changed title, updated references, minor improvements. To appear in Journal of Algebraic Combinatoric

Large Quark Rotations Neutrino Oscillations and Proton Decay

The large freedom in the SM fermionic mass matrices allows for large LH and LH quark rotations. This is a natural possibility in view of the observed large leptonic mixing. Proton decay and especially its gauge mediated decay is sensitive also to those mixing angles which are non-relevant in the SM. A model with realistic mass matrices and large rotations is presented.. It is shown that the large leptonic mixing leads to enhancement of the proton decay branching ratios involving muons.Comment: 4 pages, talk given at the SUSY'01 (held in JINR, Dubna, Russia, 11-17 June 2001), to appear in the Proceeding

Can One Phase Induce All CP Violations Including Leptogenesis?

In the framework of a SUSY SO(10) model a phase is generated spontaneously for the B-L breaking VEV. Fitting this phase to the observed CP violating K,B decays all other CP breaking effects are uniquely predicted. In particular, the amount of Leptogenesis can be explicitly calculated and found to be in the right range and sign for the BAU.Comment: 12 pages, version published in PL