I-surfaces with one T-singularity

TL;DR

This paper classifies certain stable algebraic surfaces with specific invariants and a unique T-singularity, revealing new components in their moduli space.

Contribution

It provides a classification of stable surfaces with given invariants and a unique T-singularity, identifying new moduli space components.

Findings

Identification of two divisors in the main component.

Discovery of a new irreducible component of the moduli space.

Characterization of surfaces with a non-canonical T-singularity.

Abstract

We classify normal stable surfaces with $K_X^2 = 1$, $p_g = 2$ and $q=0$ with a unique singular point which is a non-canonical T-singularity, thus exhibiting two divisors in the main component and a new irreducible component of the moduli space of stable surfaces $\overline\gothM_{1,3}$.