Stable logarithmic maps to Deligne--Faltings pairs I

Logarithmic Stable 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 Deligne–Faltings log structures (in particular simple normal crossings divisor) from the simplest case with characteristic generated by N (essentially the smooth divisor case).

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

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...

Logarithmic Structure for Stable Maps Relative to Simple Normal Crossing Divisor

P gp := {(a, b)|(a, b) ∼ (c, d) if ∃s ∈ P such that s+ a+ d = s+ b+ c}. The monoid P is called integral if the natural map P → P gp is injective. And it is called saturated if it is integral and satisfies that for any p ∈ P , if n · p ∈ P for some positive integer n then p ∈ P . A monoid P is said to be fine if it is integral and finitely generated. A monoid P is called sharp if there are no ot...