We revisit Ekedahl, Lando, Shapiro and Vainshtein’s compactification of the stack of Hurwitz covers. By drawing a connection with the Harris and Mumford stack of admissible covers we give a new geometric interpretation of boundary points of the ELSV compactification. As a byproduct we establish that this compactification holds for any algebraically closed field of sufficiently high characteristic.

We find here another (not of the CROC-type) compactification of the Kontsevich spaces K(m,n). This compactification is a Stasheff-type compactification, in particular, it is exactly the Stasheff compactification when n = 1 or m = 1. The boundary strata of this compactification are products of the spaces K(m, n) and of the Stasheff polyhedra. Then we construct a dg Lie algebra naturally associat...

In [2] we constructed homological localizations of spaces, groups, and 17"modules; here we generalize those constructions to give "factorization systems" and "homotopy factorization systems" for maps in categories. In Section 2 we recall the definition and basic properties of factorization systems, and in Section 3 we give our first existence theorem (3.1)for such systems. It can be viewed as a...

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmüller space by the action of the mapping class group gives a compactification of Mg,n. We put an analytic structure on this quotient and prove that ...

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank 1 spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or qua...

Completely regular pseudo-compact spaces have been characterized in several ways. E. Hewitt [6, pp. 68-70] has given one characterization in terms of the Stone-Cech compactification and another in terms of the zero sets of continuous functions. J. Colmez [2; no proofs included] and I. Glicksberg [4] have obtained characterizations by means of a convergence property for sequences of continuous f...