Stephen Coughlan

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math.AG2024

2-Gorenstein stable surfaces with $K_{X}^{2} = 1$ and $χ (X) = 3$

Stephen Coughlan, Marco Franciosi, Rita Pardini +1

The compactification $M_{1, 3}$ of the Gieseker moduli space of surfaces of general type with $K_{X}^{2} = 1$ and $χ (X) = 3$ in the moduli space of stable surfaces parametrises…

math.AG2024

Moduli spaces of threefolds on the Noether line

Stephen Coughlan, Yong Hu, Roberto Pignatelli +1

In this paper, we study the moduli spaces of canonical threefolds with any prescribed geometric genus $p_{g} \geq 5$ which have the smallest possible canonical volume. This minimal vo…

math.AG2023

Half canonical rings of Gorenstein spin curves of genus two

Stephen Coughlan, Marco Franciosi, Rita Pardini +1

We introduce the notion of generalised Gorenstein spin structure on a curve and we give an explicit description of the associated section ring for curves of genus two with ample ca…

2-Gorenstein stable surfaces with KX2​=1 and χ(X)=3

Moduli spaces of threefolds on the Noether line

Half canonical rings of Gorenstein spin curves of genus two

2-Gorenstein stable surfaces with $K_{X}^{2} = 1$ and $χ (X) = 3$