On T-divisors and intersections in ${\overline{M}}_{1,3}$

Abstract

The moduli space of stable surfaces with $K_X^2=1$ and $\chi (X)=3$ has at least two irreducible components that contain surfaces with T-singularities. We show that the two known components intersect transversally in a divisor. Moreover, we exhibit other new boundary divisors and study how they intersect one another.

28 pages, 8 figures