Compactifying the Jacobian

Compactifying the Relative Jacobian over Families of Reduced Curves

0.1. Motivation and Goal. The problem of finding a natural relative compactification of the relative Jacobian over a family of curves has drawn a lot of attention since Igusa’s pioneering work [18] in the fifties. (In Subsect. 0.2 the reader will find a slightly more detailed account of this history, with references.) In the case where the curves in the family are geometrically integral, a very...

Compactifying Moduli of Hyperelliptic Curves

We construct a new compactification of the moduli space Hg of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of Hg.

Compactifying the state space for alternative theories of gravity

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in R-gravity and compare to...

Genetic Order and Compactifying Garbage Collectors

Compactifying M-theory to four dimensions

We consider compactifications of M-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non constant due to the presence of sources coming from five-branes wrapping two-dimensional submanifolds of the internal seven-dimensional space. We derive the expression for the field strengths and consider an explicit...