The toric Hilbert scheme of a rank two lattice is smooth and irreducible

The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value one for every degree in the grading monoid N^n/L. In this paper we show that if L is two-dimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert scheme of a rank three lattice can be reducible.Comment: 19 pages, 4 figure

Creative Commons Licenses: empowering open access

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Using Soft Systems Methodology to Improve the Colour Forecasting Process

Colour forecasting is a process where attempts are made to accurately forecast colour for fashion-related products that consumers will purchase in the near future, usually two years ahead. Seasonal colours are recognised as a powerful driver of sales. Currently trend forecasts are marketed and sold globally. The information is broad and generalised and does not take into account colour preferences. In the study the anticipation of consumer acceptance was identified as the weakness of the process and an improved system model was developed replacing the anticipation stage with consumer colour acceptance data. The improved model is considered highly beneficial for fashion-related industries to adopt in order to increase their competitiveness in the global market and to assist waste reduction (unwanted products) that impact on the environment. In this paper the development of the two models is presented and discussed in an attempt to purposely promote the usefulness of soft systems methodology for design research

Preparing Information Literate Teachers: A Review of the Literature

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Preparing Information Literate Teachers: A Review of the Literature

Ye