By Kazuya Kato, Sampei Usui
In 1970, Phillip Griffiths expected that issues at infinity should be extra to the classifying area D of polarized Hodge buildings. during this booklet, Kazuya Kato and Sampei Usui become aware of this dream via making a logarithmic Hodge conception. They use the logarithmic constructions started by means of Fontaine-Illusie to restore nilpotent orbits as a logarithmic Hodge constitution. The booklet specializes in imperative themes. First, Kato and Usui build the high-quality moduli house of polarized logarithmic Hodge constructions with extra constructions. Even for a Hermitian symmetric area D, the current concept is a refinement of the toroidal compactifications by way of Mumford et al. For common D, fantastic moduli areas can have slits attributable to Griffiths transversality on the boundary and be not in the neighborhood compact. moment, Kato and Usui build 8 enlargements of D and describe their kin via a primary diagram, the place 4 of those enlargements reside within the Hodge theoretic quarter and the opposite 4 reside within the algebra-group theoretic region. those components are hooked up by way of a continual map given by way of the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the development within the first subject.
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Additional info for Classifying Spaces of Degenerating Polarized Hodge Structures
For example, one could improve the current precision on the forward-backward asymmetry parameter Ab by more than an order of magnitude. In Table 4, we have listed some improved measurements envisioned at the linear collider. The tin>- error on sin2 0% assumes a precise beam polarization measurement that may require polarizing both the electron and positron beams. 4 as input. One finds , 1-l i 19) where the dominant error comes from hadronic loop uncertainties in Q (assumed here to be reduced by a factor of 3 compared to the current error).
At these levels. the measurement would not only provide a stringent test of supersymmetry as a symmetr!. of Xaturc, but also it might also be sensiti\-e to radiative corrections from heavy squark and 34 ^‘- E? ,@T. 98 - I I 100 I 90 5-2000 6543A6 Figure 11: Determination production, from . 110 OW of the gbeRe coupling from a 100 fb-l measurement slepton species [80, 81, 821. 3 Chargino mass ml I of selectron pair measurement The process of chargino pair production in e+e- annihilation is somewhat more complicated than slepton pair production, but it also provides more interesting observables.
In addition, the mass differences of the partners of q~ and qR can be measured to this accuracy using polarization asymmetries . 2 for stau mixing, it is possible to measure the top squark mixing angle to better than 1% accuracy in a 500 ft-’ experiment . The second issue is the possibility of the grand unification of supersymmetry breaking parameters. This is the crucial test of whether supersymmetry breaking arises from physics above the grand unification scale or from a different mechanism acting at lower energies.
Classifying Spaces of Degenerating Polarized Hodge Structures by Kazuya Kato, Sampei Usui