An analog of the Edwards model for Jacobians of genus 2 curves

We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of the Jacobian variety than the standard version in P^{15}. We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law, with no exceptions.Comment: 33 pages, with supplemental maple file. v2: added reference

Moduli interpretation of Eisenstein series

Let L >= 3. Using the moduli interpretation, we define certain elliptic modular forms of level Gamma(L) over any field k where 6L is invertible and k contains the Lth roots of unity. These forms generate a graded algebra R_L, which, over C, is generated by the Eisenstein series of weight 1 on Gamma(L). The main result of this article is that, when k=C, the ring R_L contains all modular forms on Gamma(L) in weights >= 2. The proof combines algebraic and analytic techniques, including the action of Hecke operators and nonvanishing of L-functions. Our results give a systematic method to produce models for the modular curve X(L) defined over the Lth cyclotomic field, using only exact arithmetic in the L-torsion field of a single Q-rational elliptic curve E^0.Comment: 29 pages, amslatex. Version 6: corrected a sign misprint in equation (4.6) (thanks to N. Mascot for pointing it out). Final accepted versio

Sect and House in Syria: History, Architecture, and Bayt Amongst the Druze in Jaramana

This paper explores the connections between the architecture and materiality of houses and the social idiom of bayt (house, family). The ethnographic exploration is located in the Druze village of Jaramana, on the outskirts of the Syrian capital Damascus. It traces the histories, genealogies, and politics of two families, bayt Abud-Haddad and bayt Ouward, through their houses. By exploring the two families and the architecture of their houses, this paper provides a detailed ethnographic account of historical change in modern Syria, internal diversity, and stratification within the intimate social fabric of the Druze neighbourhood at a time of war, and contributes a relational approach to the anthropological understanding of houses