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math.AG2026
Relative completions and separating boundary divisors in moduli of curves
Ma Luo, Tatsunari Watanabe
We study relative completions of fundamental groups of moduli stacks of curves of compact type and of partial compactifications of the smooth moduli stack. For , the compac…
math.AG2026
On the universal curve with unordered marked points in positive characteristic
Ma Luo, Tatsunari Watanabe
We study the relative pro- and continuous relative completions of the algebraic fundamental groups of universal curves over the moduli stack of curves with unordered marked p…
math.AG2025
On the Universal Curves with Unordered Marked Points
Tatsunari Watanabe, Ma Luo
Over any field of characteristic , we prove that the homotopy exact sequence of algebraic fundamental groups for the universal curve with unordered marked points does not split.…