Classifying Spaces of Degenerating Polarized Hodge by Kazuya Kato, Sampei Usui

By Kazuya Kato, Sampei Usui

In 1970, Phillip Griffiths anticipated that issues at infinity might be additional to the classifying house D of polarized Hodge buildings. during this e-book, Kazuya Kato and Sampei Usui become aware of this dream by way of making a logarithmic Hodge concept. They use the logarithmic constructions started via Fontaine-Illusie to restore nilpotent orbits as a logarithmic Hodge structure.

The ebook makes a speciality of imperative issues. First, Kato and Usui build the superb moduli house of polarized logarithmic Hodge buildings with extra constructions. Even for a Hermitian symmetric area D, the current conception is a refinement of the toroidal compactifications by means of Mumford et al. For basic D, wonderful moduli areas could have slits because of Griffiths transversality on the boundary and be now not in the community compact. moment, Kato and Usui build 8 enlargements of D and describe their kinfolk via a primary diagram, the place 4 of those enlargements dwell within the Hodge theoretic quarter and the opposite 4 dwell within the algebra-group theoretic region. those components are attached by way of a continual map given via the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the development within the first topic.

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3 New 2’ bosons The new physics at the TeV it might have an even larger simplest extensions are those bosons appear as new vectors scale must have gauge symmetry with extra U(1) resonances-Z’ SU(3) x SU(2) x U(1) gauge symmetr!.. but with additional heavy vect,or particles. The gauge symmetries. The corresponding gauge bosons-coupling to lepton and to @ pairs. Extra 157(l) factors in the gauge group preserve the predictions of graud unification. 111 fact,, these new symmetries appear naturally in models in which the grand unification group is larger than the minimal choice of Sri(5).

Thus, a Higgs boson produced in e+e- t Z”ho with a rate comparable to the Standard Model rate must have these quantum numbers. However, there are a number of checks on 2s 6-2000 6543A6 Figure 6: Angular distribution of 2 boson in e+e- + Z”ho, as reconstructed sample at 300 GeV, from [69]. ble from the kinematics of Higgs production. In the limit s >> m2,,m;, a scalar Higgs boson produced in this reaction has an angular distribution da dcost? t central values. ) If the center of mass energy is not asymptotic, the corrections to these relations are predicted from kinematics.

There are many other experiments that can be done at an e+elinear collider which has sufficient energy to reach the required threshold for new particles. In this section, we will describe a number of experiments of this character. All of these experiments will eventually become relevant as components of the long-term program that we have described in Section 2. Measurements at the LHC which estimate the new thresholds could pro\-ide specific motivation for upgrading a 500 GeV collider to higher energy.

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