Classifying birationally commutative projective surfaces

Let R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3 over an uncountable algebraically closed field. Suppose that the graded quotient ring of R is a skew-Laurent ring over a field; we say that R is a birationally commutative projective surface. We classify birationally commutative projective surfaces and show that they fall into four families, parameterized by geometric data. This generalizes work of Rogalski and Stafford on birationally commutative projective surfaces generated in degree 1; our proof techniques are quite different.Comment: 60 pages; Proceedings of the LMS, 201

The Zoning in and the Zoning out of the Elderly: Emerging Community and Communication Patterns

Increasingly, senior only residences are zoning seniors out of mainstream residential areas and into segregated living and mature communities. Senior gated communities are variations on a theme of gated communities in which lifestyle is packaged and sold. Active adult retirement communities exclude the young and offer active lifestyle living, with diverse levels of senior living choices. Such an approach contrasts with policies designed to encourage aging in place. It is also distinct from Golden Age Zoning districts designed to allow affordable housing for senior citizens in a public/private partnership. Some towns have zoned public parks to establish areas for children distinct from the elderly. Simultaneously, more and more older adults are embracing the modern media environment. According to the Pew Research Center, baby boomers and seniors are the fastest growing group of social networking website users to connect with family, friends from the past, and seeking information and support with medical issues. This paper explores the person/place relationship and issues associated with design for the social needs of an aging in a media filled world

G-algebras, twistings, and equivalences of graded categories

Given Z-graded rings A and B, we study when the categories gr-A and gr-B are equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple proof of Zhang's main result. This makes the definition of a Zhang twist extremely natural and extends Zhang's results.Comment: 13 pages; typos corrected and revised slightly; to appear in Algebras and Representation Theor

How Chicago's Public Housing Transformation Can Inform Federal Policy

Chicago has long dominated the national discourse about urban poverty in general and public housing in particular, and the policy changes that affect Chicago tend to have repercussions for national policy. The Chicago Housing Authority's1999 Plan for Transformation sought to undo the mistakes of decades of federal policy that had left Chicago and too many other cities blighted by large, decaying public housing properties. Although other cities like Atlanta and San Francisco followed suit, the CHA's Plan was the first -- and largest -- citywide public housing transformation initiative, representing an enormous investment of public and private resources.In many respects, the CHA's story shows the potential of public housing transformation: attractive new developments, better quality of life for most residents, and a better-functioning housing authority. However, the CHA's story also raises cautions about the limitations and the potential risks of this bold -- and costly -- approach and about what else it will take to help address the problems of deep poverty that keep too many public housing families from moving toward self-sufficiency

Geometric idealizers

Let X be a projective variety, $\sigma$ an automorphism of X, L a $\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right ideal of sections vanishing at Z. We study the subring R = k + I of B. Under mild conditions on Z and $\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal. We give geometric conditions on Z and $\sigma$ that determine the algebraic properties of R, and show that if Z and $\sigma$ are sufficiently general, in a sense we make precise, then R is left and right noetherian, has finite left and right cohomological dimension, is strongly right noetherian but not strongly left noetherian, and satisfies right $\chi_d$ (where d = \codim Z) but fails left $\chi_1$. We also give an example of a right noetherian ring with infinite right cohomological dimension, partially answering a question of Stafford and Van den Bergh. This generalizes results of Rogalski in the case that Z is a point in $\mathbb{P}^d$.Comment: 43 pages; comments welcom

Barriers to Investment by Russian Firms: Property Protection or Credit Constraints?

A multitude of explanations for low investment by Russian firms have been offered: high inflation, high interest rates, falling production, falling GDP, an underdeveloped banking system, a confiscatory tax regime, calls for the re-nationalization of industry, excessive regulations, and an underdeveloped legal system, among others. This paper's basic premise is that investment in Russia will not occur if firms are unable to ensure the security of their property and property rights; that is, if the risk of destruction or expropriation is high. Nor will investment occur if access to investment funds is limited. Data collected from 264 Russian firms in the spring and fall 2001 are used to construct a security index and credit index in order to evaluate the relative importance of property protection and access to financing on the investment activities of manufacturing, retail, and other service sector firms in Moscow, Rostov, Taganrog, and Vladivostok. For the firms participating in this survey, the reported percentage of profit reinvested is significantly higher among firms which responded positively to questions about the effectiveness of police and courts in protecting their property and property rights, and significantly lower among firms which made above-average payments (official and unofficial) for property protection. Unofficial payments alone lower investment by 20%. Firms with access to credit reported reinvesting a significantly greater share of their profits. All other things equal, firms in Moscow, and firms in food processing and food distribution reinvested a significantly greater share of their profits. Manufacturing firms reported reinvesting a significantly smaller share of their profits in comparison to retail shops or other service sector companies. These results do not vary with the amount of collateral a firm has; that is, whether the firm owns or leases its premises.http://deepblue.lib.umich.edu/bitstream/2027.42/39853/3/wp469.pd