The compactified jacobian can be nonreduced

We prove by explicit example that the compactified jacobian can be nonreduced. The example is a rational space curve of arithmetic genus 4. This answers a question posed by Cyril D'Souza in 1979.Comment: Final versio

Autoduality holds for a degenerating abelian variety

We prove that certain degenerate abelian varieties, the compactified Jacobian of a nodal curve and a stable quasiabelian variety, satisfy autoduality. We establish this result by proving a comparison theorem that relates the associated family of Picard schemes to the N\'eron model, a result of independent interest. In our proof, a key fact is that the total space of a suitable family of compactified Jacobians has rational singularities.Comment: To appear in Research in Mathematical Sciences. Material reorganized and typos correcte

Extensions of the universal theta divisor

The Jacobian varieties of smooth curves fit together to form a family, the universal Jacobian, over the moduli space of smooth marked curves, and the theta divisors of these curves form a divisor in the universal Jacobian. In this paper we describe how to extend these families over the moduli space of stable marked curves (or rather an open subset thereof) using a stability parameter. We then prove a wall-crossing formula describing how the theta divisor varies with the stability parameter. We use that result to analyze a divisor on the moduli space of smooth marked curves that has recently been studied by Grushevsky-Zakharov, Hain and M\"uller. In particular, we compute the pullback of the theta divisor studied in Alexeev's work on stable abelic varieties and in Caporaso's work on theta divisors of compactified Jacobians.Comment: 42 pages, 5 figures. Final version. Added Section 4.1, which describes how divisor classes other than the theta divisor var

Comparison of polybrominated diphenyl ethers (PBDEs) and polychlorinated biphenyls (PCBs) in the serum of hypothyroxinemic and euthyroid dogs.

ObjectiveTo determine the profile of 14 polybrominated diphenyl ethers (PBDEs) and 23 polychlorinated biphenyls (PCBs) in serum of domestic canines and whether this was predictive of thyroid hormone status.SamplesSerum samples were collected from 51 client-owned dogs visiting the University of California Davis William R. Pritchard Veterinary Medical Teaching Hospital during 2012 to 2016 for routine appointments. Fifteen dogs were diagnosed with hypothyroxinemia while 36 were euthyroid.ProceduresConcentrations of PBDEs and PCBs in canine serum samples were measured by gas chromatography mass spectrometry. Logistic regression analysis was used to determine the association between the presence/absence of canine hypothyroxinemia and the serum concentration of individual PBDE or PCB congeners.ResultsThe median concentrations of total PBDE and PCB congeners in the hypothyroxinemic group were 660 and 1,371 ng/g lipid, respectively, which were higher than concentrations detected in the control group. However, logistic regression analysis determined that current concentrations of PBDEs and PCBs in canines were not significantly associated with hypothyroxinemia. BDE 183 was the only congener showing near significance (p = 0.068).ConclusionsPBDE and PCB congeners were detected in all canine samples confirming ongoing exposure to these pollutants. Because household dogs share the human environment, they may serve as biosentinels of human exposure to these contaminants