Logarithmic Stable Maps to Deligne–faltings Pairs Ii

Stable Logarithmic Maps to Deligne–faltings Pairs Ii

We make an observation which enables one to deduce the existence of an algebraic stack of log maps for all generalized Deligne– Faltings log structures (in particular simple normal crossings divisor) from the simplest case with characteristic generated by N (essentially the smooth divisor case).

Logarithmic Maps to Deligne-faltings Pairs

Higher-dimensional Analogues of Stable Curves

The Minimal Model Program offers natural higher-dimensional analogues of stable n-pointed curves and maps: stable pairs consisting of a projective variety X of dimension ≥ 2 and a divisor B, that should satisfy a few simple conditions, and stable maps f : (X, B) → Y . Although MMP remains conjectural in higher dimensions, in several important situations the moduli spaces of stable pairs, genera...

Forgetful Maps between Deligne-mostow Ball Quotients

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimension...

On (log) Twisted Curves

We describe an equivalence between the notion of balanced twisted curve introduced by Abramovich and Vistoli, and a new notion of log twisted curve, which is a nodal curve equipped with some logarithmic data in the sense of Fontaine and Illusie. As applications of this equivalence, we construct a universal balanced twisted curve, prove that a balanced twisted curve over a general base scheme ad...