• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.929-949
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• 2022

Given an ACM set 𝕏 of points in a multiprojective space ℙ^m×ℙⁿ over a field of characteristic zero, we are interested in studying the Kähler different and the Cayley-Bacharach property for 𝕏. In ℙ¹×ℙ¹, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the Kähler different. However, this result fails to hold in ℙ^m×ℙⁿ for n > 1 or m > 1. In this paper we start an investigation of the Kähler different and its Hilbert function and then prove that 𝕏 is a complete intersection of type (d₁, …, d_m, d'₁, …, d'_n) if and only if it has the Cayley-Bacharach property and the Kähler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of 𝕏 under certain assumptions.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.35 no.1
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• pp.107-115
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• 2019

This research explores a historical trajectory of the Milwaukee Art Museum from its establishment to the third expansion over the last six decades. After established in 1957 by the architect, Eero Saarinen, this museum underwent three expansions led by three different architects including, David Kahler, Santiago Calatrava, and James Shields. Reasons for expanding the museum were varied. A lack of exhibition space, an absence of visual identity, and path interruption problem within urban contexts were the main factors of a series of expansion. Furthermore, this research points out that there are three issues in the process of the expansion. The first is connection issues between the downtown and the lakefront in which the museum has blocked the public flow. The second, there were controversies on the allocation of the expanded space among the main body of the decision including architects, curators, and stakeholders. The last one is relationships among architects. This is related to each architect's attitude toward the museum. Drawing on historical documents and interviews with the regional architects, I argue that the identity and values of the museum have changed over time through the expansions rather than having the invariable.