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

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

Rejoinder

Rejoinder of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]Comment: Published in at http://dx.doi.org/10.1214/11-STS337REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org