16 citations · 25 across the 7 of their papers we have counts for
8 papers
Quartic surfaces up to volume preserving equivalence
Tom Ducat
We study log Calabi--Yau pairs of the form , where is a quartic surface, and classify all such pairs of coregularity less than or equal to one, up to volume p…
The tropicalisation of a -flop
Tom Ducat
As a standard example in toric geometry, the Atiyah flop of a -curve in a smooth 3-fold can be described combinatorially in terms of the two possible triangulations of a s…
The 3-dimensional Lyness map and a self-mirror log Calabi-Yau 3-fold
Tom Ducat
The 2-dimensional Lyness map is a 5-periodic birational map of the plane which may famously be resolved to give an automorphism of a log Calabi-Yau surface, given by the complement…
Constructing Fano 3-folds from cluster varieties of rank 2
Stephen Coughlan, Tom Ducat
Cluster algebras give rise to a class of Gorenstein rings which enjoy a large amount of symmetry. Concentrating on the rank 2 cases, we show how cluster varieties can be used to co…
The decomposition groups of plane conics and plane rational cubics
Tom Ducat, Isac Hedén, Susanna Zimmermann
The decomposition group of an irreducible plane curve is the subgroup of birational maps which restrict to a…
Constructing Q-Fano 3-folds à la Prokhorov & Reid
Tom Ducat
We generalise a construction by Prokhorov & Reid of two families of Q-Fano 3-folds of index 2 to obtain five more families of Q-Fano 3-folds; four of index 2 and one of index 3. Tw…
Divisorial extractions from singular curves in a smooth 3-fold, II: low codimension
Tom Ducat
Following the first paper, we continue to study Mori extractions from singular curves centred in a smooth 3-fold. We treat the case where the divisorial extraction exists in relati…
Divisorial Extractions from Singular Curves in Smooth 3-Folds, I
Tom Ducat
Consider a singular curve contained in a smooth 3-fold . Assuming the general elephant conjecture, the general hypersurface section is Du Val. Under th…