Stable logarithmic maps to Deligne-Faltings pairs II

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...

Skeletons of stable maps II: superabundant geometries

We implement new techniques involving Artin fans to study the realizability of tropical stable maps in superabundant combinatorial types. Our approach is to understand the skeleton of a fundamental object in logarithmic Gromov–Witten theory—the stack of prestable maps to the Artin fan. This is used to examine the structure of the locus of realizable tropical curves and derive three principal co...