Effective reconstruction of generic genus 4 curves from their theta hyperplanes

Effective reconstruction formulas of a curve from its theta hyperplanes are known classically in genus 2 (where the theta hyperplanes are Weierstrass points), and 3 (where, for a generic curve, the theta hyperplanes are bitangents to a plane quartic). However, for higher genera, no formula or algorithm are known. In this paper we give an explicit (and simple) algorithm for computing a generic genus 4 curve from it's theta hyperplanes.Comment: no content modification to previous version; presentation modification following referees comment

Formulas for the arithmetic geometric mean of curves of genus 3

The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.Comment: 26 pages, amslatex, xypic +2 eps figure

Prime property institutions for a subprime era: Toward innovative models of homeownership

This Article breaks new ground toward contractual and institutional innovation in models of homeownership, equity building, and mortgage enforcement. Inspired by recent developments in the affordable housing sector and other types of public financing schemes, we suggest extending institutional and financial strategies such as time- and place-based division of property rights, conditional subsidies, and credit mediation to alleviate the systemic risks of mortgage foreclosure. Two new solutions offer a broad theoretical basis for such developments in the economic and legal institution of homeownership: a for-profit shared equity scheme led by local governments alongside a private market shared equity model, one of "bootstrapping home buying with purchase options".property, homeownership, mortgage, finance, local government, subsidy, tax.

Rescaling City Property

This Article seeks to identify the growing tension between the contemporary physical and digital reality of cities across the world and the formal, often archaic, body of norms that governs city powers and duties vis-à-vis different types of persons and corporations: locals, non-local residents of the same nation-state, and foreigners. The nation-state’s continuing dominance, both in the domestic division of power across various legal systems and in the international arena, often results in a systemic mismatch

Temporary Eminent Domain

Times of emergency call for drastic measures. These steps may include the physical takeover of privately-owned assets by the government for a certain period of time and for various purposes, aimedat addressing the state of emergency. When will such acts amount to a taking, and what compensation should be paid to the property owner? How do temporary physical appropriations during times of emergencydiverge, if at all, from temporary takeovers in more ordinary times? The doctrinal and theoretical analysis of potential temporary takings has been done mostly in the context of non-physical government intervention with private property, such as when a local government imposes a temporary moratorium on land development until a certain condition is met. This Article focuses, however, on less investigatedscenarios of temporary physical takeovers or other forms of governmentinvasions. It seeks to identify the differences between a temporary invasion and a permanent occupation of property considered a per se taking under the Loretto rule. In so doing, this Article argues that whilethe alleged distinction between prevention of public harm and promotionof public benefit often proves untenable in evaluating whether a permanent government measure constitutes a taking, it might make moresense in exploring temporary acts. Temporary eminent domain—referring here to various types of actsamounting to time-limited physical takings, even if not initially recognized as such by the government—may diverge from permanenteminent domain in yet another key element: identifying the basis for justcompensation. Under long established (although often criticized) rules, compensation for a permanent taking is based on identifying the “fair market value” of the rights taken, while ignoring the effects that the public use for which the underlying asset is taken might have on the property’s long-term value. The allegedly parallel metric used in the case of temporary takings,one of “fair rental value,” may often prove inadequate, both practically and normatively. This Article argues that because of unique aspects of temporary physical takings, legal rules on compensation should often seek to identify lost profits or actual damage. Moreover, in some cases, in which there is a direct relation between the pre-appropriation use of the asset and its post-appropriation use by the government, justcompensation might also be based on a certain portion of the value of thepublic use. This is especially so when the time-sensitive value of the assetduring such public use is particularly high. On this point, the Article offers an analogy to rules pertaining to compulsory licenses for patents